# Publications

Below, the publications related to the project are listed based on publication channel.

Preprint

Journal

Conference

Books

The following papers have been submitted for publication, and are currently in preprint.

- R.B. Christensen, O. Geil: On nested code pairs from the Hermitian curve. [Preprint]
- I. Cascudo, J.S. Gundersen, D. Ruano: Improved Bounds on the Threshold Gap in Ramp Secret Sharing. [preprint]
- R.B. Christensen: On one-round reliable message transmission. [preprint]
- C. Galindo, F. Hernando, D. Ruano: Classical and Quantum Evaluation Codes at the Trace Roots. [preprint].
- C. Galindo, O. Geil, F. Hernando, D. Ruano: New binary and ternary LCD codes. [preprint].
- I. Cascudo: On squares of cyclic codes. [preprint].
- O. Geil, U. Martínez-Peñas: Bounding the number of common zeros of multivariate polynomials and their consecutive derivatives, 26 pages. [preprint].
- O. Geil, F. Özbudak: On affine variety codes from the Klein quartic, 27 pages. [preprint].
- O. Geil, F. Özbudak, D. Ruano: Constructing sequences with high nonlinear complexity from Hermitian function fields, 10 pages.
- I. Cascudo, B. David: SCRAPE: Scalable Randomness Attested by Public Entities. [preprint].
- U. Martínez-Peñas: Communication efficient and strongly secure secret sharing schemes based on algebraic geometry codes. [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]

The following papers are published in peer-reviewed journals.

- U. Martínez-Peñas, R. Matsumoto: Relative generalized matrix weights of matrix codes for universal security on wire-tap networks. To appear in IEEE Transactions on Information Theory. [preprint]
- U. Martínez-Peñas: Generalized rank weights of reducible codes, optimal cases and related properties. Accepted for publication in IEEE Transactions on Information Theory. [preprint] [paper]
- O. Geil, S. Martin, U. Martínez-Peñas, R. Matsumoto, D. Ruano: On asymptotically good ramp secret sharing schemes. Accepted for publication in IEICE Trans. Fundamentals. [preprint]
- C. Galindo, O. Geil, F. Hernando, D. Ruano: Improved constructions of nested code pairs. Accepted for publication in IEEE Transactions on Information Theory. [preprint] [paper]
- C. Galindo, O. Geil, F. Hernando, D. Ruano: On the distance of stabilizer quantum codes from J-affine variety codes. Quantum Information Processing, Volumen 16, Issue 4, 16:111 (2017). [preprint] [paper]
- U. Martínez-Peñas: Rank equivalent and rank degenerate skew cyclic codes, Advances in Mathematics of Communications, 11 (2), pages 267-282, (2017). [preprint] [paper]
- U. Martínez-Peñas: On the roots and minimum rank distance of skew cyclic codes, Designs, Codes and Cryptography, 83 (3), pages 639-660 (2017). [postprint] [paper]
- U. Martínez-Peñas, R. Pellikaan: Rank error-correcting pairs, Designs, Codes and Cryptography, 84 (1-2), pages 261-281, (2017). [postprint] [paper]
- O. Geil, S. Martin: Relative generalized Hamming weights of q-ary Reed-Muller codes, Advances in Mathematics of Communications. Volume 11, Issue 3, pages 503-531 (2017). [postprint] [paper]
- O. Geil, C. Thomsen: More results on the number of zeros of multiplicity at least r. Discrete Mathematics. Vol. 340, Issue 5, pages 1028-1038 (2017). [preprint] [paper]
- O. Geil, S. Martin, U. Martínez-Peñas, D. Ruano: Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth's second tower. 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]

The following papers are published in peer-reviewed conference proceedings.

- I. Cascudo, R.B. Christensen, J.S. Gundersen: Actively Secure OT-Extension from q-ary Linear Codes. To appear at SCN18. [preprint]
- I. Cascudo, B. David: SCRAPE: Scalable Randomness Attested by Public Entities. Applied Cryptography and Network Security (ACNS 2017), Springer Lecture Notes in Computer Science, Volume 10355, pages 537-556 (2017) [preprint] [paper].
- I. Cascudo, I. Damgård, O. Farràs and Samuel Ranellucci: Resource-efficient OT combiners with active security. Accepted at Theory of Cryptography (TCC 2017) [preprint].
- R. Matsumoto, D. Ruano: Geometric and Computational Approach to Classical and Quantum Secret Sharing. In: Applications of Computer Algebra. ACA 2015. Kotsireas I., Martínez-Moro E. (eds). Springer Proceedings in Mathematics & Statistics, vol 198. Springer (2017). [paper]
- O. Geil, F. Özbudak: Bounding the minimum distance of affine variety codes using symbolic computations of footprints. Lecture Notes in Computer Science. 5th International Castle Meeting on Coding Theory and Applications. ICMCTA 2017: Coding Theory and Applications, pages 128-138 (2017). [paper]
- O. Geil, D. Lucani: Random network coding over composite fields. Lecture Notes in Computer Science. 5th International Castle Meeting on Coding Theory and Applications. ICMCTA 2017: Coding Theory and Applications, pages 118-127 (2017). [paper]
- U. Martínez-Peñas: Universal secure rank-metric coding schemes with optimal communication overheads. Accepted for publication and presentation in ISIT 2017-The IEEE International Symposium on Information Theory, June 25-30, Aachen, Germany. [preprint]
- I. Cascudo, I. Damgård, F. Lacerda, S. Ranellucci: Oblivious Transfer from any Non-Trivial Elastic Noisy Channels via Secret Key Agreement. TCC2016-B. Proceedings, Part I. Springer-Verlag Lecture Notes in Computer Science, Volume 9985, pages 204-234, (2016). [preprint] [paper]
- I. Cascudo, I. Damgård, B. David, N. Döttling and J. Buus Nielsen: Rate-1, Linear Time and Additively Homomorphic UC Commitments. CRYPTO 2016 . Advances in Cryptology-CRYPTO 2016, Part III, Springer-Verlag Lecture Notes in Computer Science, Volume 9816, pages 179-207 (2016) [preprint] [paper]
- 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]

Book Chapters:

- 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]

Books:

- 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]