Publications

The following papers are published in peer-reviewed journals.

• R.B. Christensen, O. Geil: Steane-Enlargement of Quantum Codes from the Hermitian Function Field. Designs, Codes and Cryptography. [preprint] [paper]
• I. Cascudo, J.S. Gundersen, D. Ruano: Squares of Matrix-product Codes. Finite Fields and their Applications.[preprint] [paper]
• O. Geil, F. Özbudak: On affine variety codes from the Klein quartic. Cryptography and Communications. [preprint] [paper]
• O. Geil, U. Martínez-Peñas: Bounding the number of common zeros of multivariate polynomials and their consecutive derivatives. Combinatorics, probability & computing. [preprint] [paper]
• O. Geil, F. Özbudak, D. Ruano: Constructing sequences with high nonlinear complexity from Hermitian function fields. Semigroup Forum [paper]
• R.B. Christensen: On one-round reliable message transmission. Information Processing Letters, Vol. 147; July 2019. [preprint] [paper][postprint]
• I. Cascudo, J.S. Gundersen, D. Ruano: Improved Bounds on the Threshold Gap in Ramp Secret Sharing. IEEE Transactions on Information Theory. [preprint] [paper]
• C. Galindo, F. Hernando, D. Ruano: Classical and Quantum Evaluation Codes at the Trace Roots. IEEE Transactions on Information Theory. [preprint] [paper] .
• I. Cascudo: On squares of cyclic codes. IEEE Transactions on Information Theory, 2018. [preprint] [paper]
• C. Galindo, O. Geil, F. Hernando, D. Ruano: New binary and ternary LCD codes. [preprint] [paper]
• U. Martínez-Peñas: Communication efficient and strongly secure secret sharing schemes based on algebraic geometry codes. [preprint] [paper]
• U. Martínez-Peñas, R. Matsumoto: Relative generalized matrix weights of matrix codes for universal security on wire-tap networks. IEEE Transactions on Information Theory, volume 64, no. 4. April 2018. [preprint] [paper]
• 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. Security and Cryptography for Networks. SCN 2018. Lecture Notes in Computer Science, vol 11035. [preprint] [paper]
• I. Cascudo, R. Cramer, C. Xing, C. Yuan: Amortized Complexity of Information-Theoretically Secure MPC Revisited. CRYPTO 2018. Lecture Notes in Computer Science, vol 10993. [preprint] [paper]
• 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]