• Skjernvej 4, A, 1-210

    9220 Aalborg Ø

    Denmark

  • Niels Jernes Vej 10, B-026

    9220 Aalborg Ø

    Denmark

19992020

Research output per year

If you made any changes in Pure these will be visible here soon.

Research Output

2020

Foreword—Special Issue: Codes, Cryptology and Curves in honour of Ruud Pellikaan

Beelen, P., Geil, O., Martínez-Moro, E. & Wu, X. W., 1 Aug 2020, In : Designs, Codes, and Cryptography. 88, 8, p. 1477-1478 2 p.

Research output: Contribution to journalEditorialResearchpeer-review

Open Access

On nested code pairs from the Hermitian curve

Christensen, R. B. & Geil, O., 2020, In : Finite Fields and Their Applications. 68, 26 p., 101742.

Research output: Contribution to journalJournal articleResearchpeer-review

Open Access

On Steane-enlargement of quantum codes from Cartesian product point sets

Christensen, R. B. & Geil, O., 22 May 2020, In : Quantum Information Processing. 19, 7, 15 p., 192.

Research output: Contribution to journalJournal articleResearchpeer-review

Open Access

Steane-enlargement of quantum codes from the Hermitian function field

Christensen, R. B. & Geil, O., 11 Feb 2020, In : Designs, Codes and Cryptography. 88, 8, p. 1639-1652 14 p.

Research output: Contribution to journalJournal articleResearchpeer-review

Open Access
1 Citation (Scopus)
2019

Accelerated processing for maximum distance separable codes using composite extension fields

Ruano, D., Lucani, D. E. & Geil, O., 1 Jan 2019, European Wireless 2019 Conference, EW 2019. VDE Verlag GMBH, p. 14-18 5 p. (European Wireless 2019 Conference, EW 2019).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

Bounding the number of common zeros of multivariate polynomials and their consecutive derivatives

Geil, H. O. & Martinez Peñas, U., 1 Mar 2019, In : Combinatorics, Probability & Computing. 28, 2, p. 253-279 27 p.

Research output: Contribution to journalJournal articleResearchpeer-review

Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve

Geil, H. O., Ozbudak, F. & Ruano Benito, D., 2019, In : Semigroup Forum. 98, p. 543-555 13 p.

Research output: Contribution to journalJournal articleResearchpeer-review

Open Access
File
9 Downloads (Pure)

New binary and ternary LCD codes

Galindo, C., Geil, H. O., Hernando, F. & Ruano Benito, D., 1 Feb 2019, In : I E E E Transactions on Information Theory. 65, 2, p. 1008-1016 9 p., 8356685.

Research output: Contribution to journalJournal articleResearchpeer-review

Open Access
File
7 Citations (Scopus)
94 Downloads (Pure)

On affine variety codes from the Klein quartic

Geil, H. O. & Ozbudak, F., 15 Mar 2019, In : Cryptography and Communications. 11, 2, p. 237-257 21 p.

Research output: Contribution to journalJournal articleResearchpeer-review

1 Citation (Scopus)
2018

Fulcrum: Flexible Network Coding for Heterogeneous Devices

Lucani, D. E., Pedersen, M. V., Ruano Benito, D., Sørensen, C. W., Fitzek, F. H. P., Heide, J., Geil, H. O., Nguyen, V. & Reisslein, M., Nov 2018, In : IEEE Access. 6, p. 77890-77910 18 p.

Research output: Contribution to journalJournal articleResearchpeer-review

Open Access
File
8 Citations (Scopus)
178 Downloads (Pure)

Improved constructions of nested code pairs

Galindo, C., Geil, H. O., Hernando, F. & Ruano Benito, D., 1 Apr 2018, In : I E E E Transactions on Information Theory. 64, 4, p. 2444-2459 16 p.

Research output: Contribution to journalJournal articleResearchpeer-review

6 Citations (Scopus)
2017

Bounding the Minimum Distance of Affine Variety Codes Using Symbolic Computations of Footprints

Geil, H. O. & Ozbudak, F., 2017, Coding Theory and Applications: 5th International Castle Meeting, ICMCTA 2017, Vihula, Estonia, August 28-31, 2017, Proceedings. Barbero, Á. I., Skachek, V. & Ytrehus, Ø. (eds.). Springer VS, p. 128-138 11 p. (Lecture Notes in Computer Science, Vol. 10495).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

3 Citations (Scopus)

List decoding algorithm based on voting in Gröbner bases for general one-point AG codes

Matsumoto, R., Ruano Benito, D. & Geil, H. O., 2017, In : Journal of Symbolic Computation. 79, Part 2, p. 384-410 27 p.

Research output: Contribution to journalJournal articleResearchpeer-review

Open Access

More results on the number of zeros of multiplicity at least r

Geil, H. O. & Thomsen, C., May 2017, In : Discrete Mathematics. 340, 5, p. 1028-1038 11 p.

Research output: Contribution to journalJournal articleResearchpeer-review

2 Citations (Scopus)

On asymptotically good ramp secret sharing schemes

Geil, H. O., Martin, S., Martinez Peñas, U., Matsumoto, R. Y. & Ruano Benito, D., 2017, In : IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. E100-A, 12, p. 2699-2708 10 p.

Research output: Contribution to journalJournal articleResearchpeer-review

2 Citations (Scopus)

On the distance of stabilizer quantum codes from J-affine variety codes

Galindo, C., Geil, H. O., Hernando, F. & Ruano Benito, D., 2017, In : Quantum Information Processing. 16, 4, 32 p., 111.

Research output: Contribution to journalJournal articleResearchpeer-review

8 Citations (Scopus)

Random Network Coding over Composite Fields

Geil, H. O. & Lucani, D. E., 2017, Coding Theory and Applications: 5th International Castle Meeting, ICMCTA 2017, Vihula, Estonia, August 28-31, 2017, Proceedings. Barbero, Á. I., Skachek, V. & Ytrehus, Ø. (eds.). Springer VS, p. 118-127 10 p. (Lecture Notes in Computer Science; No. 10495).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth's second tower

Geil, H. O., Martin, S., Martinez Peñas, U. & Ruano Benito, D., 2017, In : Journal of Algebra Combinatorics Discrete Structures and Applications. 4, 1, p. 37-47 11 p.

Research output: Contribution to journalJournal articleResearchpeer-review

Open Access
File
133 Downloads (Pure)

Relative Generalized Hamming Weights of q-ary Reed-Muller Codes

Geil, H. O. & Martin, S., 2017, In : Advances in Mathematics of Communication. 11, 3, p. 503-531 29 p.

Research output: Contribution to journalJournal articleResearchpeer-review

6 Citations (Scopus)
2016

Fejlkorrigerende koder

Geil, H. O., 2016

Research output: Non-textual formSound/Visual production (digital)Education

Open Access

More results on the number of zeros of multiplicity at least r

Geil, H. O. & Thomsen, C., 2016, ArXiv, 14 p.

Research output: Working paperResearch

More results on the number of zeros of multiplicity at least r

Geil, H. O. & Thomsen, C., 2016, ArXiv, 14 p.

Research output: Working paperResearch

On asymptotically good ramp secret sharing schemes

Geil, H. O., Martin, S., Martinez Peñas, U., Matsumoto, R. & Ruano Benito, D., 2016, ArXiv, 28 p.

Research output: Working paperResearch

On the distance of stabilizer quantum codes from J-affine variety codes

Galindo, C., Geil, H. O., Hernando, F. & Ruano Benito, D., 2016, ArXiv, 26 p.

Research output: Working paperResearch

2015

An improvement of the Feng-Rao bound for primary codes

Geil, H. O. & Martin, S., 2015, In : Designs, Codes and Cryptography. 76, 1, p. 49-79 31 p.

Research output: Contribution to journalJournal articleResearchpeer-review

4 Citations (Scopus)

On asymptotically good ramp secret sharing schemes

Geil, H. O., Martin, S., Martinez Peñas, U., Matsumoto, R. & Ruano Benito, D., 2015, Proceedings of the WCC 2015. 10 p.

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth's second tower

Geil, H. O., Martin, S., Martinez Peñas, U. & Ruano Benito, D., 2015, 21st Conference on Applications of Computer Algebra: ACA 2015. p. 120-124 5 p.

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

Open Access

Roots and coefficients of multivariate polynomials over finite fields

Geil, H. O., Jul 2015, In : Finite Fields and Their Applications. 34, p. 36-44 9 p.

Research output: Contribution to journalJournal articleResearchpeer-review

2014

Affine variety codes are better than their reputation

Geil, H. O. & Martin, S., 2014, Proceedings of the 21st Symposium on Mathematical Theory of Networks and Systems. University of Groningen, p. 362-365 4 p. TuA04.3

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

File
101 Downloads (Pure)

Erratum: On the second weight of generalized Reed-Muller codes

Geil, H. O., Oct 2014, In : Designs, Codes and Cryptography. 73, 1, p. 267 1 p.

Research output: Contribution to journalComment/debateResearchpeer-review

Further improvements on the Feng-Rao bound for dual codes

Geil, H. O. & Martin, S., Nov 2014, In : Finite Fields and Their Applications. 30, p. 33-48 16 p.

Research output: Contribution to journalJournal articleResearchpeer-review

2 Citations (Scopus)

Relative generalized Hamming weights of one-point algebraic geometric codes

Geil, H. O., Martin, S., Matsumoto, R., Ruano, D. & Luo, Y., Oct 2014, In : I E E E Transactions on Information Theory. 60, 10, p. 5938 - 5949 12 p.

Research output: Contribution to journalJournal articleResearchpeer-review

25 Citations (Scopus)

Relative generalized Hamming weights of one-point algebraic geometric codes

Geil, H. O., Martin, S., Matsumoto, R. & Ruano, D., 2014, Proceedings of Information Theory Workshop (ITW), 2014 IEEE. IEEE Press, p. 137-141 5 p. (IEEE Information Theory Workshop).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

3 Citations (Scopus)
2013

Aspects of random network coding

Geil, H. O. & Thomsen, C., 2013, Algebraic geometry modeling in information theory. Moro, E. M. (ed.). World Scientific, p. 47-81 35 p. (Series on Coding Theory and Cryptology, Vol. 8).

Research output: Contribution to book/anthology/report/conference proceedingBook chapterResearchpeer-review

Feng-Rao decoding of primary codes

Geil, H. O., Matsumoto, R. & Ruano, D., 2013, In : Finite Fields and Their Applications. 23, p. 35-52 18 p.

Research output: Contribution to journalJournal articleResearchpeer-review

14 Citations (Scopus)

Generalization of the Lee-O'Sullivan list decoding for one-point AG codes

Matsumoto, R., Ruano, D. & Geil, H. O., 2013, In : Journal of Symbolic Computation. 55, p. 1-9 9 p.

Research output: Contribution to journalJournal articleResearchpeer-review

1 Citation (Scopus)

Weighted Reed-Muller codes revisited

Geil, H. O. & Thomsen, C., 2013, In : Designs, Codes and Cryptography. 66, 1-3, p. 195-220 26 p.

Research output: Contribution to journalJournal articleResearchpeer-review

20 Citations (Scopus)
2012

A new method for constructing small-bias spaces from Hermitian codes

Geil, H. O., Martin, S. & Matsumoto, R., 2012, Arithmetic of Finite Fields: 4th International Workshop on , WAIFI 2012. Özbudak, F. & Rodríguez-Henríquez, F. (eds.). Springer, Vol. 7369. p. 29-44 16 p. (Lecture Notes in Computer Science, Vol. 7369).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

List decoding algorithms based on Gröbner bases for general one-point AG codes

Geil, H. O., Matsumoto, R. & Ruano, D., Jul 2012, Information Theory Proceedings (ISIT): 2012 IEEE International Symposium on Information Theory. IEEE, p. 86-90 5 p. (Proceedings of the IEEE International Symposium on Information Theory).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

8 Citations (Scopus)
2011

List decoding of a class of affine variety codes

Geil, H. O. & Thomsen, C., Apr 2011, The Seventh International Workshop on Coding and Cryptography 2011. Paris: Institut National de Recherche en Informatique et en Automatique, Vol. 7. p. 263-272 10 p.

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

On the order bounds for one-point AG codes

Geil, H. O., Munuera, C., Ruano Benito, D. & Torres, F., 2011, In : Advances in Mathematics of Communication. 5, 3, p. 489-504 16 p.

Research output: Contribution to journalJournal articleResearchpeer-review

27 Citations (Scopus)
2010

On the order bounds for one-point AG codes

Geil, H. O., Munuera, C., Ruano Benito, D. & Torres, F., 25 Feb 2010

Research output: Other contributionNet publication - Internet publicationResearch

2009

Algebraic geometry codes from order domains

Geil, H. O., 2009, Gröbner Bases, Coding and Cryptography. Sala, M. (ed.). Springer, p. 121-141 21 p.

Research output: Contribution to book/anthology/report/conference proceedingBook chapterResearch

11 Citations (Scopus)

A note on the injection distance

Bulygin, S., Geil, H. O. & Ruano Benito, D., 9 Dec 2009

Research output: Other contributionNet publication - Internet publicationResearch

Bounding the number of Fq-rational places in algebraic function fields using Weierstrass semigroups

Geil, H. O. & Matsumoto, R., 2009, In : Journal of Pure and Applied Algebra. 213, 6, p. 1152-1156 5 p.

Research output: Contribution to journalJournal articleResearchpeer-review

8 Citations (Scopus)

On the number of zeros of multiplicity r

Geil, H. O. & Thomsen, C., 8 Dec 2009

Research output: Other contributionNet publication - Internet publicationResearch

Evaluation Codes from an Affine Veriety Code Perspective

Geil, H. O., 2008, Advances In Algebraic Geometry Codes. Moro, E. M., Gómez, C. M. & Benito, D. R. (eds.). World Scientific, p. 153-181 29 p. (Coding Theory and Cryptology, Vol. 5).

Research output: Contribution to book/anthology/report/conference proceedingBook chapterResearch

Evaluation Codes from Order Domain Theory

Andersen, H. E. & Geil, H. O., 2008, In : Finite Fields and Their Applications. 14, 1, p. 92-123

Research output: Contribution to journalJournal articleResearchpeer-review

37 Citations (Scopus)