News | Research Interests | Members | Workshops | Networks | Activities | Publications |

- Umberto Martínez-Peñas has received an
*EliteForsk*travel grant of 200.000 kr in connection with his research visit at Massachusetts Institute of Technology - MIT. [Interview] - Ignacio Cascudo will join the Mathematics for communication research group on April 2016 as an Assistant professor.
- The Danish Mathematics for Communication Community has been granted 2.509.920 Dkr from The Danish Council for Independent Research - Natural Science for the project "How secret is a secret?". Principal investigator is Olav Geil. [Webpage of the project]
- Workshop on Applications of Algebraic Geometry in Secret Sharing and Coding Theory, Aalborg, June 30th 2014.

Since Shannon's seminal paper in 1948 the theory of communication has grown into a huge area. It encompasses different topics such as error-correcting codes, cryptography, secret sharing, steganography, source coding, and network coding. A broad range of mathematics is involved in the study including algebra, linear algebra, computer algebra, algebraic geometry, combinatorics, and probability theory. Furthermore, many communication structures can be considered as mathematical subjects in their own right. Also, the study of communication theory often leads to developments in purely theoretical areas. This, for instance, is the case for the theory of finite fields and related structures, and also for computer algebra.

- Performance of toric, affine variety, and algebraic geometry codes.
- Decoding algorithms.
- Applications of Gröbner basis theory.
- Multivariate polynomials over finite fields.
- Network coding.
- Algebraic function field theory.
- Secret sharing schemes.
- Code based cryptography.

- René B. Christensen (PhD student) works on secret sharing.
- Olav Geil (Professor MSO) works on affine variety and algebraic geometry codes. He studies their parameters, their decoding algorithms and their applications in secret sharing schemes. Olav also takes an interest in multivariate polynomials over finite fields and in algebraic function field theory. Furthermore, he works on network coding.
- Ignacio Cascudo (assistant professor) works on cryptography, mainly in the areas of secure multiparty computation and secret sharing, and is especially interested in the applications of algebra, algebraic geometry and coding theory to those areas.
- Tom Høholdt (Adjunct Professor) works on Algebraic Coding Theory, Sequence Design, Signal Analysis and other Areas of Applied (Discrete) Mathematics.
- Umberto Martínez-Peñas (PhD student) works on algebraic geometry codes. He studies their parameters and their application in secret sharing schemes.
- Diego Ruano (Associate professor) works on algebraic coding theory, which includes aspects of algebraic function fields, algebraicgeometry codes and decoding algorithms. Diego also studies code-based cryptography, secret sharing and network coding.
- Jaron Skovsted Gundersen (PhD student) works on secret sharing.

- Stefano Martin (PhD student and Research assistant) worked on affine variety codes and algebraic geometry codes. He studied their parameters and their applications in secret sharing schemes.

**Workshops**

- Workshop "Secrets", workshop of the research project "How secret is a secret?", DTU Compute, The technical University of Denmark, November 14th 2016.
- Workshop on Applications of Algebraic Geometry in Secret Sharing and Coding Theory, Aalborg, June 30th 2014.
- Skagen Workshop: 4th AGINCC workshop, July 28th – 31st 2013

- The Network Coding Focus Group of Aalborg University.
- The COST Action IC1104-Random Network Coding and Designs over GF(q). Olav Geil and Diego Ruano are Management committee substitute members.
- The Danish-Chinese Center for Applications of Algebraic Geometry in Coding Theory and Cryptography (AGINCC).
- We collaborate with the coding theory group at DTU, Peter Beelen, and with Johan P. Hansen at Aarhus University.

**Future activities**

- Diego Ruano will visit Jaume I University, Castellón, Spain, to do research with Carlos Galindo and Fernando Hernando, December 18th - 23th, 2016.
- Fernando Hernando at Jaume I University (Castellón, Spain) will visit Aalborg University as guest professor for one month, June 2017.

**Past activities (since 2013)**

- The film "Olav Geil: Fejlkorrigerende koder" has been released as part of the series "10 danske matematikere-10 matematiske fort ællinger", Lindhardt og Ringhof, Uddannelse. The film is available from https://www.youtube.com/watch?v=rIszlgH7Exw
- We have organized and participated in the workshop "Secrets", workshop of the research project "How secret is a secret?", DTU Compute, The technical University of Denmark, November 14th 2016.
- On November 4, 2016 the film "Fejlkorrigerende koder" was presented in connection with a reception at the publishing house Lindhardt og Rinhof. The film is one out ten in the series "10 danske matematikere -- 10 matematiske fortællinger". In the film Olav Geil lectures on coding theory to an audience of highschool student.
- Umberto Martínez-Peñas has visited Frank R. Kschischang at University of Toronto (Canada), November 1st 2016 - March 15th 2017.
- U. Martínez-Peñas has given a talk at the Research seminar in coding theory and cryptography. University of Neuchatel, Switzerland, October 26th 2016.
- René B. Christensen and Jaron Skovsted Gundersen have started a PhD at Aalborg University (4+4 scheme) under the supervision of Ignacio Cascudo and Diego Ruano.
- Olav Geil is a member of the Scientific Committee for 5th International Castle Meeting on Coding Theorey and Applications, to take place in Estonia, August 28--31, 2017.
- U. Martínez-Peñas has participated and given a talk at 54th Annual Allerton Conference on Communication, Control, and Computing. September 27th - 30th , 2016, Allerton Park and Retreat Center, Monticello, IL, USA
- Ignacio Cascudo has been a tutorial speaker at Workshop on Mathematics of Information - Theoretic Cryptography. National University of Singapore and Nanyang Technological University (Singapore), September 19th - 30th, 2016.
- Olav Geil gave an inaugural lecture on August 30th 2016 in connection with his appointment as a professor with special responsibilities. The title of the lecture was "Bounding the number of affine roots - with applications in reliable and secure communication". [Slides].
- T. Høholdt has participated and U. Martínez-Peñas has participated and given a talk at ISIT 2016-IEEE International Symposium on Information Theory, Barcelona, Spain. July 10th - 15th 2016.
- T. Høholdt has participated (invited) and U. Martínez-Peñas has participated and given a talk at WCM 2016-Workshop on Mathematics in Communications, Santander, Spain. July 6th - 8th 2016.
- Ignacio Cascudo is publicity co-chair for International Conference on Information-Theoretical Cryptography, August 9-12, 2016.
- Ignacio Cascudo participated in Paris Crypto Day, ENS, June 30th, 2016.
- Ignacio Cascudo was an invited speaker and had an invited paper at Computability in Europe (CiE 2016). Université Paris 13, Paris, June 27th - July 1st, 2016. [paper]
- Olav Geil was invited speaker at Workshop: On the Algebraic and Geometric Classifications of Projective Varieties, June 20-24, 2016 at University of Messina. Title of talk: "Bounding the number of affine roots using algebraic methods", abstract.
- Ferruh Özbudak at Middle East Technical University (Turkey) has visited Aalborg University as guest professor, June 15th - July 15th 2016.
- Ruud Pellikaan at Eindhoven University of Technology (The Netherlands) has visited Aalborg University as guest professor, June 3rd - 15th 2016.
- Ignacio Cascudo participated in Workshop on Theory and Practice of Secure Multiparty Computation. Aarhus University, May 30- June 3, 2016.
- Olav Geil has visited Jaume I University, Castellón, Spain to do research with Carlos Galindo and Fernando Hernando, May 22th - June 5th, 2016.
- Diego Ruano has participated and gave a talk at the Third IMAC and Singacom Day on Algebraic Applications to Information Theory, Castellón, Spain, May 9th - 10th, 2016.
- Diego Ruano has visited Jaume I University, Castellón, Spain to do research with Carlos Galindo and Fernando Hernando, May 6th - 21th, 2016.
- T. Høholdt visited University of Puerto Rico for research collaboration with H. Janwa and F. Pinero.
- T. Høholdt visited J. Justesen in Washington, D.C. in May 2016 to work on the revised version of their book.
- Since April 15th, Olav Geil is a Professor MSO for 5 years.
- On April 11th 2016, Peter Beelen visited Aalborg University to do research with Olav Geil and Diego Ruano.
- Daniel E. Lucani has given a talk at at the COST Action IC1104 conference Network Coding and Designs, Dubrovnik, Croatia, April 4th - 9th, 2016. "Composite extension fields for (network) coding: Designs and opportunities. Joint work with Olav Geil, Diego Ruano, Janus Heide.
- Umberto Martínez-Peñas participated and gave two talks at the COST Action IC1104 conference Network Coding and Designs, Dubrovnik, Croatia, April 4th - 9th, 2016.
- Ignacio Cascudo participated and gave a talk and Olav Geil and Umberto Martínez-Peñas participated at the symposium on the 60th birthday of Ivan Damgård, Aarhus, April 1st - 2nd, 2016.
- Umberto Martínez-Peñas has received an
*EliteForsk*travel grant of 200.000 kr in connection with his research visit at Massachusetts Institute of Technology - MIT. [Interview] - On February 24th, Olav Geil visited Tom Høholdt at DTU.
- On February 12th 2016, Peter Beelen has visited Aalborg University.
- On February 1st, 2016, Tom Høholdt and Olav Geil gave a talk at Information Meeting for The Danish National Research Foundation at Aalborg University.
- Stefano Martin started working for Seluxit on February 1st.
- Diego Ruano has supervised the following master thesis at Aalborg University: McEliece, kodebaseret kryptografi og matrixprodukt-koder, Camilla Lund Melander and Ida Bentzen-Petersen, January 2016.
- Olav Geil is participating in the
*forskningslederkursus*at CBS-Copenhagen Business School. - On December 14th 2015, Olav Geil has visited the Technical University of Denmark to do research with Peter Beelen.
- Olav Geil has been a member of the committee for the PhD defense of Nhut Nguyen. Advisor: Peter Beelen. DTU (Denmark), December 14th 2015.
- On November 27th 2015, Vitaly Skachek (University of Tartu, Estonia) has visited Aalborg university.
- Olav Geil and Diego Ruano have participated in the workshop DARNEC'15 Design and Application of Random Network Codes, Istanbul Technical University, Turkey, 4th - 6th November 2015.
- On October 28th 2015, Ignacio Cascudo (Aarhus University) has visited Aalborg university to do research. [Photo 1] [Photo 2]
- Umberto Martínez-Peñas has given a talk at the Young Researchers Conference of the Royal Spanish Mathematical Society Murcia, Spain, September 7th - 11th, 2016.
- Diego Ruano has participated and presented a work at the Workshop on Algebra and Geometry 2015, University of Valladolid, Spain 2nd - 4th September 2015.
- Stefano Martin and Diego Ruano have participated and presented a work at ACA 2015-Applications of Computer Algebra. Kalamata, Greece, July 20th - 23rd, 2015.
- On June 19th 2015, Olav Geil has visited the Technical University of Denmark to do research with Peter Beelen.
- On June 18th 2015, Peter Beelen has visited Aalborg University to do research with Diego Ruano.
- Fernando Hernando at Jaume I University (Castellón, Spain) has visited Aalborg University as guest professor, June 18th - July 18th 2015.
- Ruud Pellikaan from Eindhoven University of Technology, The Netherlands, has visited Aalborg University May 29th - June 16th, 2015.
- Sudhir R. Ghorpade from IIT-Bombay, Mumbai India, has visited Aalborg University May 28th - 31st, 2015.
- Umberto Martínez-Peñas participated in the 2015 European School of Information Theory (ESIT), IEEE Information Theory Society, Zandvoort, The Netherlands, April 20th - 24th, 2015
- On April 14th 2015, Peter Beelen has visited Aalborg University Copenhagen (Sydhavn campus) to do research with Diego Ruano.
- Olav Geil participated, and Umberto Martínez-Peñas participated and presented a work at WCC 2015-The Ninth International Workshop on Coding and Cryptography. Paris, France, April 13th - 17th, 2015.
- Tom Høholdt is a member of the program committee of the workshop WCC 2015-The Ninth International Workshop on Coding and Cryptography. Paris, France, April 13th - 17th, 2015.
- On February 24th 2015, Peter Beelen has visited Aalborg university to do research with Olav Geil.
- Diego Ruano has visited Ryutaroh Matsumoto at the Tokyo Institute of Technology (Japan), February 21st - March 10th 2015. Partly supported by the "Program for promoting the enhancement of research universities" at Tokyo Institute of Technology.
- On February 10th 2014, Peter Beelen has visited the Aalborg University Copenhagen to do research with Diego Ruano.
- Stefano Martin, research assistant at Aalborg University, has been associated to this project.
- Umberto Martínez-Peñas has participated in the SP Coding and Information School. Campinas, Brazil. January 19th - 30th 2015.
- Olav Geil has been a member of the committee for the PhD defense of Fernando Piñero. Advisors: Peter Beelen and Tom Høholdt. DTU (Denmark), December 16th 2014.
- Stefano Martin (supervisor Olav Geil and co-supervisor Diego Ruano) has defended his Ph.D. thesis at Aalborg University on the 8th of December 2014. Tom Høholdt was a member of the committee.
- On December 3rd 2014, Olav Geil, VELUX visiting professor Ryutaroh Matsumoto and Diego Ruano have visited the Technical University of Denmark to do research with Peter Beelen.
- Stefano Martin's contract at Aalborg University has been extended. He will continue working as Research assistant with the Mathematics for communication group until January 2016.
- VELUX visiting professor Ryutaroh Matsumoto from the Tokyo Institute of Technology has given a PhD course at Aalborg University. Title: Welcome to Quantum Information Processing. November 21st - December 1st 2014. [Slides] [Group photo] [Almost a group photo...]
- VELUX visiting professor Ryutaroh Matsumoto from the Tokyo Institute of Technology has given a talk at Aarhus University. Title: Quantum Ramp Secret Sharing. November 19th 2014. [Slides]
- On November 10th 2014, Peter Beelen has visited Aalborg university to do research with Olav Geil, VELUX visiting professor Ryutaroh Matsumoto and Diego Ruano.
- Olav Geil has participated and gave a talk in the IEEE Information Theory Workshop-ITW2014, Hobart, Tasmania, Australia, November 2nd - 5th 2014.
- On October 9th 2014, Olav Geil and VELUX visiting professor Ryutaroh Matsumoto have visited the Technical University of Denmark to do research with Peter Beelen.
- Diego Ruano has been a member of the committee for the PhD defense of Wilson Olaya-León: Hamming weights' of castle codes. Advisor: Carlos Munuera. University of Valladolid (Spain), October 1st 2014.
- Stefano Martin has started at Aalborg University to work with the Mathematics for communication group as Research Assistant. He will work at Aalborg University between 1st October 2014 – 31st December 2014.
- Ryutaroh Matsumoto from the Tokyo Institute of Technology has visited Aalborg University during fall 2014 as VELUX Visiting Professor. [Photo with Network Coding Focus Group]
- Olav Geil has participated in the 4th International Castle Meeting on Coding Theory and Applications, Castle of Palmela, Portugal, September 15th - 18th, 2014.
- Diego Ruano has participated and gave a talk in the INdAM meeting: International meeting on numerical semigroups - Cortona 2014, Cortona, Italy, September 8th - 13th, 2014.
- On September 1st 2014, Umberto Martínez-Peñas has started a PhD at Aalborg University funded by the FNU project "How secret is a secret?". His supervisor is Olav Geil and his co-supervisor is Diego Ruano.
- Diego Ruano has visited Carlos Galindo and Fernando Hernando at Jaume I University (Castellón, Spain), July 2014.
- Diego Ruano participated and gave a talk in the Second IMAC and Singacom Day on Algebraic Applications to Information Theory. Castellón, Spain, July 17th, 2014.
- Stefano Martin participated and gave a talk in The 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). Groningen, The Netherlands, July 7th - 11th, 2014.
- We participated and gave a talk in the Workshop on Applications of Algebraic Geometry in Secret Sharing and Coding Theory, Aalborg, June 30th 2014.
- Olav Geil and Diego Ruano are participated in NetCod 2014 - International Symposium on Network Coding. Aalborg, Denmark June 27th - 28th, 2014. Olav Geil was a member of the Technical program committee.
- Stefano Martin participated and presented a poster in the 2014 European School of Information Theory. Tallinn, Estonia, April 14th - 18th, 2014.
- Diego Ruano gave a talk in the ATENEO seminar of IMUVA center. University of Valladolid, Spain, March 20th, 2014.
- Olav Geil participated and gave a talk in the International Conference on Algebraic Geometry and Coding Theory. Mumbai, India, December 2nd - 6th, 2013.
- Olav Geil participated and gave a talk in the workshop Algebraic curves over finite fields. Special Semester on Applications of Algebra and Number Theory. Linz, Austria, November 11th -15th, 2013.
- Diego Ruano and gave a talk in the GAS seminar of the SINGACOM group. University of Valladolid, Spain, October 17th, 2013.
- Olav Geil and Diego Ruano participated in the Conference on Random network codes and Designs over GF(q). Ghent, Belgium, September 18th - 20th, 2013.
- The Mathematics for Communication research group organized the Skagen Workshop: 4th AGINCC workshop. July 28th – 31st 2013.
- Stefano Martin participated and gave a talk in the workshop ACA 2013-Applications of Computer Algebra. Malaga, Spain, July 2nd-6th, 2013.
- Yuan Luo from Shanghai Jiao Tong University (Shanghai, China) has visited Aalborg University, July 1st - 31st 2013.
- Olav Geil participated and gave a talk in the Zurich COST Meeting - Random Network Coding and Designs over GF(q). Zurich, Switzerland, June 20th-21st, 2013.
- Fernando Hernando from Jaume I University (Castellón, Spain) has visited Aalborg University, June 6th - July 11th 1013.
- Olav Geil participated and gave a talk in the workshop Mathematics of Information-Theoretic Cryptography. Lorentz Center, Leiden, The Netherlands, May 21st - 25th, 2013.
- Stefano Martin stayed 3 months (March-May) at East China Normal University (Shanghai, China) visiting Hao Chen.
- Diego Ruano participated and gave a talk in the RSME Workshop 2013-Spanish Mathematical Society Biannual Workshop. Santiago de Compostela, Spain, January 21st - 25th, 2013.

**Publications**

- U. Martínez-Peñas: Communication efficient and strongly secure secret sharing schemes based on algebraic geometry codes. [preprint]
- C. Galindo, O. Geil, F. Hernando, D. Ruano: Improved constructions of nested code pairs. [preprint]
- C. Galindo, O. Geil, F. Hernando, D. Ruano: On the distance of stabilizer quantum codes from J-affine variety codes. [preprint]
- U. Martínez-Peñas: Generalized rank weights of reducible codes, optimal cases and related properties. [preprint]
- D.E. Lucani, M.V. Pedersen, D. Ruano, C.W. Sørensen, F.H.P. Fitzek, J. Heide, O. Geil: Fulcrum Network Codes: A Code for Fluid Allocation of Complexity. [preprint]
- O. Geil, S. Martin, U. Martínez-Peñas, R. Matsumoto, D. Ruano: On asymptotically good ramp secret sharing schemes. [preprint]

- O. Geil, C. Thomsen: More results on the number of zeros of multiplicity at least r, to appear in Discrete Mathematics. [preprint]
- U. Martínez-Peñas: Rank equivalent and rank degenerate skew cyclic codes, to appear in Advances in Mathematics of Communications. [preprint]
- U. Martínez-Peñas: On the roots and minimum rank distance of skew cyclic codes, to appear in Designs, Codes and Cryptography. [postprint] [paper]
- U. Martínez-Peñas, R. Pellikaan: Rank error-correcting pairs, to appear in Designs, Codes and Cryptography. [postprint] [paper]
- O. Geil, S. Martin: Relative generalized Hamming weights of q-ary Reed-Muller codes, to appear in Advances in Mathematics of Communications. [postprint]
- O. Geil, S. Martin, U. Martínez-Peñas, D. Ruano: Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth's second tower. Accepted for publication in Journal of Algebra Combinatorics Discrete Structures and Applications, Volume 4, Issue 1, pages 37-47 (2017) [postprint] [paper]
- R. Matsumoto, D. Ruano, O. Geil: List decoding algorithm based on voting in Gröbner bases for general one-point AG codes. Journal of Symbolic Computation Volume 79, Part 2, pages 384–410 (2017). [postprint] [paper]
- U. Martínez-Peñas: On the similarities between rank and Hamming weights and their applications to network coding. IEEE Transaction on Information Theory, 62 (7) : 4081-4095 (2016) [postprint] [paper]
- C. Galindo, F. Hernando, D. Ruano: Stabilizer quantum codes from J-affine variety codes and a new Steane-like enlargement. Quantum Information Processing, Volume 14, Issue 9, pages 3211-3231 (2015). [postprint] [paper]
- C. Galindo, F. Hernando, D. Ruano: New quantum codes from evaluation and matrix-product codes. Finite Fields and their Applications. Volume 36, pages 98-120 (2015). [postprint] [paper]
- O. Geil, S. Martin: An improvement of the Feng-Rao bound for primary codes. Designs, Codes and Cryptography, Volume 76, Issue 1, pages 49-79 (2015), [postprint] [paper]
- T. Høholdt, F. Piñero, P. Zeng: Optimal codes as Tanner codes with cyclic component codes. Designs, Codes and Cryptography, Volume 76, Issue 1, pages 37-47 (2015). [paper]
- O. Geil: Roots and coefficients of multivariate polynomials over finite fields. Finite Fields and Their Applications, Volume 34, pages 36-44 (2015). [preprint] [paper]
- O. Geil, S. Martin, R. Matsumoto, D. Ruano, Y. Luo: Relative generalized Hamming weights of one-point algebraic geometric codes. IEEE Transactions on Information Theory, vol.60, no. 10, pages 5938-5949 (2014). [preprint] [paper]
- T. Høholdt, J. Justesen: On the sizes of expander graphs and minimum distances of graph codes. Discrete Mathematics, Volume 325, pages 38-46 (2014) [paper]
- O. Geil, S. Martin: Further improvements on the Feng-Rao bound for dual codes. Finite Fields and their Applications, Volume 30, pages 33-48 (2014). [postprint] [paper]
- I. Márquez-Corbella, E. Martínez-Moro, G.R. Pellikaan, D. Ruano: Computational Aspects of Retrieving a Representation of an Algebraic Geometry Code. Journal of Symbolic Computation, Volume 64, pages 67-87 (2014). [postprint] [paper]
- O. Geil, R. Matsumoto, D. Ruano: Feng-Rao decoding of primary codes. Finite Fields and their Applications, Volume 23, pages 35–52 (2013). [postprint] [paper]
- F. Hernando, M. O'Sullivan, D. Ruano: List decoding of repeated codes. Applicable Algebra in Engineering, Communication and Computing. Volume 24, Issue 3-4, pages 237-253 (2013). [postprint] [paper]
- R. Matsumoto, D. Ruano, O. Geil: Generalization of the Lee-O'Sullivan list decoding for one-point AG codes. Journal of Symbolic Computation, Volume 55, pages 1-9 (2013). [postprint] [paper]
- F. Hernando, D. Ruano: Decoding of matrix-product codes. Journal of Algebra and its Applications, Volume 12, Issue 4, Article ID 1250185, 15 pages (2013). [postprint] [paper]
- P. Beelen, D. Ruano: Bounding the number of points on a curve using a generalization of Weierstrass semigroups. Designs, Codes and Cryptography, Volume 66, Issue 1-3, pages 221-230 (2013). [postprint] [paper]
- O. Geil, C. Thomsen: Weighted Reed-Muller codes revisited. Designs, Codes and Cryptography, Vol. 66, pp. 195-220 (2013). [postprint] [paper]
- F. Hernando, T. Høholdt, D. Ruano: List decoding of matrix-product codes from nested codes: an application to quasi-cyclic codes. Advances in Mathematics of Communications (AMC), Volume 6, Issue 3, pages 259-272 (2012). [postprint] [paper]
- O. Geil, C. Munuera, D. Ruano, F. Torres: On the order bounds for one-point AG codes. Advances in Mathematics of Communications (AMC), Volume 5, Issue 3, pages 489-504 (2011). [postprint] [paper]
- F. Hernando, D. Ruano: New linear codes from matrix-product codes with polynomial units. Advances in Mathematics of Communications (AMC), Volume 4, Issue 3, pages 363-367 (2010). [postprint] [paper]
- O. Geil, R. Matsumoto: Bounding the number of rational places using Weierstrass semigroups. Journal of Pure and Applied Algebra, 213, (6), pp. 1152-1156 (2009) [extended version] [paper]
- F. Hernando, K. Lally, D. Ruano: Construction and decoding of matrix-product codes from nested codes. Applicable Algebra in Engineering, Communication and Computing, Volume 20, Issue 5, pages 497-507 (2009). [postprint] [paper]
- D. Ruano: On the structure of generalized toric codes. Journal of Symbolic Computation, Volume 44, Issue 5, pages 499-506 (2009). [postprint] [paper]
- O. Geil: On the second weight of generalized Reed-Muller codes. Design, Codes and Cryptography, pp. 323-330 (2008). [postprint] [paper]
- H.E. Andersen, O. Geil: Evaluation Codes from Order Domain Theory. Finite Fields and Their Applications Vol. 14 (1), pp. 92-123 (2008). [postprint] [paper]
- D. Ruano: On the parameters of r-dimensional toric codes. Finite Fields and their Applications, Volume 13, Issue 4, pages 962-976 (2007). [postprint] [paper]
- D. Ruano: Computing the Feng-Rao distances for codes from order domains. Journal of Algebra (Computational algebra section), Volume 309, Issue 2, pages 672-682 (2007). [postprint] [paper]
- O. Geil: On Codes from Norm-Trace Curves. Finite Fields and Their Applications (9), pp. 351-371 (2003). [postprint] [paper]
- O. Geil, R. Pellikaan: On the Structure of Order Domains. Finite Fields and Their Applications (8), pp. 369-396 (2002). [postprint] [paper]
- O. Geil, T. Høholdt: Footprints or Generalized Bezout's Theorem. IEEE Trans. on Inform. Theory, March 2000, pp. 635-641 (2000). [postprint] [paper]

- I. Cascudo, I. Damgård, F. Lacerda, S. Ranellucci: Oblivious Transfer from any Non-Trivial Elastic Noisy Channels via Secret Key Agreement. Accepted por publication and presentation at TCC2016-B. [preprint]
- I. Cascudo, I. Damgård, B. David, N. Döttling and J. Buus Nielsen: Rate-1, Linear Time and Additively Homomorphic UC Commitments. Accepted for publication and presentation at CRYPTO 2016 . [preprint]
- U. Martínez-Peñas, R. Matsumoto: Unifying Notions of Generalized Weights for Universal Security on Wire-Tap Networks. 54th Annual Allerton Conference on Communication, Control, and Computing. September 27th - 30th , 2016, Allerton Park and Retreat Center, Monticello, IL, USA
- U. Martínez-Peñas: Generalized rank weights of reducible codes, optimal cases and related properties. IEEE International Symposium on Information Theory, Barcelona, Spain, July 10-15, 2016. [preprint] [paper]
- U. Martínez-Peñas: Rank equivalent and rank degenerate skew cyclic codes. Workshop on Mathematics and Communications, Santander, Spain, July 6-8, 2016. [preprint]
- O. Geil, S. Martin, U. Martínez-Peñas, D. Ruano: Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth's second tower. Accepted for publication and presentation at ACA 2015-Applications of Computer Algebra. Kalamata, Greece, July 20th - 23rd, 2015.
- C. Galindo, F. Hernando, D. Ruano: Quantum codes with bounded minimum distance. Accepted for publication and presentation at ACA 2015-Applications of Computer Algebra. Kalamata, Greece, July 20th - 23rd, 2015.
- R. Matsumoto, D. Ruano: Geometric and Computational Approach to Classical and Quantum Secret Sharing. Accepted for publication and presentation at ACA 2015-Applications of Computer Algebra. Kalamata, Greece, July 20th - 23rd, 2015.
- D.Gomez-Perez, O. Moreno,T. Høholdt, I. Rubio, A.Z. Tirkel: Linear Complexity for Multidimensional Arrays-a Numerical Invariant. Information Theory Proceedings (ISIT), 2015 IEEE International Symposium on, pages 86-90 (2015). [paper]
- O. Geil, S. Martin, U. Martínez-Peñas, R. Matsumoto, D. Ruano: On asymptotically good ramp secret sharing schemes. Accepted for publication and presentation in WCC-2015. The Ninth International Workshop on Coding and Cryptography (2015).
- O. Geil, S. Martin, R. Matsumoto, D. Ruano, Y. Luo: Relative generalized Hamming weights of one-point algebraic geometric codes. In Proceedings of Information Theory Workshop (ITW), 2014 IEEE, pages 137-141 (2014). [paper]
- O. Geil, S. Martin: Affine variety codes are better than their reputation. Proceedings of The 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). Groningen, The Netherlands, 4 pages (2014).
- O. Geil, S. Martin, R. Matsumoto: A new method for constructing small-bias spaces from Hermitian codes. Proceedings of WAIFI-2012, Lecture Notes in Computer Science, LNCS 7369, pp. 29-44 (2012). [postprint] [paper]
- O. Geil, R. Matsumoto, D. Ruano: List decoding algorithms based on Gröbner bases for general one-point AG codes. Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on, pages 86-90 (2012). [postprint] [paper]
- O. Geil, C. Thomsen: List decoding of a class of affine variety codes. Proceedings of WCC-2011, Paris, Ed. by D. Augot and A. Canteaut pp. 263-272 (2011).
- P. Beelen, D. Ruano: The order bound for toric codes. Applied algebra, algebraic algorithms, and error-correcting codes, Lecture Notes in Computer Science, 5527. Springer, Berlin, pages 1-10 (2009). [postprint] [paper]
- O. Geil, R. Matsumoto and C. Thomsen: On Field Size and Success Probability in Network Coding. Proc. of WAIFI-2008, Lecture Notes in Comput. Sci., Springer Verlag, pp. 157-173 (2008). [postprint] [paper]
- O. Geil, R. Matsumoto: Generalized Sudan's list decoding for order domain codes. Proc. of AAECC-17, Lecture Notes in Comput. Sci., LNCS 4851, Springer-Verlag, pp. 50-59 (2007). [postprint] [paper]
- O. Geil and C. Thommesen: On the Feng-Rao Bound for Generalized Hamming Weights. Proc. AAECC-16, Lecture Notes in Comput. Sci., Vol. LNCS 3857, Springer-Verlag, Berlin pp. 295-306 (2006). [postprint] [paper]
- O. Geil, T. Høholdt: On Hyperbolic Codes. Proc. AAECC-14, LNCS 2227, Springer-Verlag, pp. 159-171 (2001). [paper]

- O. Geil, C. Thomsen: Aspects of random network coding. Published in "Algebraic Geometry Modeling in Information Theory," World Scientific (Series on Coding Theory and Cryptography), Edited by Edgar Martinez-Moro, pp. 47-81 (2013). [paper]
- E. Martínez-Moro, D. Ruano: Mattson Solomon transform and algebra codes. In Gröbner Bases, Coding, and Cryptography, pages 385-388. Editors: M. Sala, T. Mora, L. Perret, S. Sakata, C. Traverso. Springer Verlag. ISBN: 978-3-540-93805-7 (2009). [paper]
- O. Geil: Algebraic geometry codes from order domains. In Gröbner Bases, Coding, and Cryptography, pages 121-141. Editors: M. Sala, T. Mora, L. Perret, S. Sakata, C. Traverso. Springer Verlag. ISBN: 978-3-540-93805-7 (2009). [postprint] [paper]
- E. Martínez-Moro, D. Ruano: Toric codes. Chapter 8 in Advances in Algebraic Geometry Codes, pages 295-322. Series on Coding Theory and Cryptography - Vol. 5. World Scientific. ISBN 978-981-279-400-0 (2008). [paper]
- O.Geil: Evaluation Codes from an Affine Variety Code Perspective. Advances in Algebraic Geometry Codes, pages 153-180. Series on Coding Theory and Cryptography - Vol. 5. World Scientific. Eds.: E. Martinez-Moro, C. Munuera, D. Ruano (2008). [postprint] [paper]

- E. Martínez-Moro, C. Munuera, D. Ruano: editors of the book, Advances in Algebraic Geometry Codes. Series on Coding Theory and Cryptography - Vol. 5, 452 pages. World Scientific. ISBN 978-981-279-400-0 (2008). [ebook]
- E. Martínez-Moro, C. Munuera, D. Ruano: Gröbner bases: Applications to Algebraic Coding Theory (in Spanish). Venezuelan School of Mathematics, 125 pages. Edited by Venezuelan Mathematical Society, ISBN: 978-980-261-087-7 (2007). [ebook]