• 794 Citations
1988 …2019

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2019

Entanglement-assisted quantum codes from algebraic geometry codes

Fernandes Pereira, F., Pellikaan, R., Gadioli La Guardia, G. & de Assis, F. M., 2019, In : arXiv. 21 p., 1907.06357v1.

Research output: Contribution to journalArticleAcademic

Open Access
File
7 Downloads (Pure)
2018

Defining the q-analogue of a matroid

Jurrius, R. P. M. J. & Pellikaan, G. R., 13 Jul 2018, In : The Electronic Journal of Combinatorics. 25, 3, 32 p., #P3.2.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
4 Citations (Scopus)
20 Downloads (Pure)

Linear codes over Fq are equivalent to LCD codes for q>3

Carlet, C., Mesnager, S., Tang, C., Qi, Y. & Pellikaan, R., 1 Apr 2018, In : IEEE Transactions on Information Theory. 64, 4, p. 3010-3017 8 p.

Research output: Contribution to journalArticleAcademicpeer-review

44 Citations (Scopus)
2017

Cryptanalysis of McEliece cryptosystem based on algebraic geometry codes and their subcodes

Couvreur, A., Marquez-Corbella, I. & Pellikaan, G. R., Aug 2017, In : IEEE Transactions on Information Theory. 63, 8, p. 5404-5418 15 p., 7942048.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
11 Citations (Scopus)
63 Downloads (Pure)

Error-correcting pairs for a public-key cryptosystem

Pellikaan, G. R. & Marquez-Corbella, I., 12 Jun 2017, In : Journal of Physics: Conference Series. 855, 1, 10 p., 012032.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
2 Citations (Scopus)
50 Downloads (Pure)

On defining generalized rank weights

Jurrius, R. & Pellikaan, G. R., 1 Feb 2017, In : Advances in Mathematics of Communications. 11, 1, p. 225-235 11 p.

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

Rank error-correcting pairs

Martinez-Penas, U. & Pellikaan, G. R., Jul 2017, In : Designs, Codes and Cryptography. 84, 1-2, p. 261-281 21 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
1 Citation (Scopus)
45 Downloads (Pure)
2016

A characterization of MDS codes that have an error correcting pair

Pellikaan, G. R. & Marquez-Corbella, I., Jul 2016, In : Finite Fields and their Applications. 40, p. 224-245 22 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
2 Citations (Scopus)
45 Downloads (Pure)
2015

Error-correcting pairs : a new approach to code-based cryptography

Márquez-Corbella, I. & Pellikaan, G. R., 2015, In : ACM Communications in Computer Algebra. 49, 1, p. 21-21

Research output: Contribution to journalArticleAcademicpeer-review

The extended and generalized rank weight enumerator of a code

Jurrius, R. P. M. J. & Pellikaan, G. R., 2015, In : ACM Communications in Computer Algebra. 49, 1, p. 21-21

Research output: Contribution to journalArticleAcademicpeer-review

2014

Computational aspects of retrieving a representation of an algebraic geometry code

Márquez-Corbella, I., Martínez-Moro, E., Pellikaan, G. R. & Ruano, D., 2014, In : Journal of Symbolic Computation. 64, p. 67-87 21 p.

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)

On the unique representation of very strong algebraic geometry codes

Márquez-Corbella, I., Martínez-Moro, E. & Pellikaan, G. R., 2014, In : Designs, Codes and Cryptography. 70, 1-2, p. 215-230 16 p.

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)
2013

The non-gap sequence of a subcode of a generalized Reed-Solomon code

Márquez-Corbella, I., Martínez-Moro, E. & Pellikaan, G. R., 2013, In : Designs, Codes and Cryptography. 66, 1, p. 317-333

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)
1 Downloads (Pure)
2012

Truncation formulas for invariant polynomials of matroids and geometric lattices

Jurrius, R. P. M. J. & Pellikaan, G. R., 2012, In : Mathematics in Computer Science. 6, 2, p. 121-133

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
1 Citation (Scopus)
73 Downloads (Pure)
2010

Foreword (Special issue on Algebraic coding theory and applications)

Campillo, A., Fitzpatrick, P., Martínez-Moro, E. & Pellikaan, G. R., 2010, In : Journal of Symbolic Computation. 45, 7, p. 721-722

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
2 Downloads (Pure)
2009

Bounded distance decoding of linear error-correcting codes with Gröbner bases

Bulygin, S. & Pellikaan, G. R., 2009, In : Journal of Symbolic Computation. 44, 12, p. 1626-1643

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)
2008

Extractors for binary elliptic curves

Rezaeian Farashahi, R., Pellikaan, G. R. & Sidorenko, A., 2008, In : Designs, Codes and Cryptography. 49, 1-3, p. 171-186

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)
2006

A symmetric Roos bound for linear codes

Duursma, I. M. & Pellikaan, G. R., 2006, In : Journal of Combinatorial Theory, Series A. 113, 8, p. 1677-1688

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
8 Citations (Scopus)
1 Downloads (Pure)
2004

List decoding of q-ary Reed-Muller codes

Pellikaan, G. R. & Wu, X. W., 2004, In : IEEE Transactions on Information Theory. 50, 4, p. 679-682

Research output: Contribution to journalArticleAcademicpeer-review

42 Citations (Scopus)
1 Downloads (Pure)
2003

Integral closures and weight functions over finite fields

Leonard, D. A. & Pellikaan, G. R., 2003, In : Finite Fields and their Applications. 9, 4, p. 479-504 26 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
7 Citations (Scopus)
2002

On the structure of order domains

Geil, O. & Pellikaan, G. R., 2002, In : Finite Fields and their Applications. 8, 3, p. 369-396

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
48 Citations (Scopus)
2001

On the existence of order functions

Pellikaan, G. R., 2001, In : Journal of Statistical Planning and Inference. 94, 2, p. 287-301

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)
2000

The Newton polygon of plane curves with many rational points

Beelen, P. H. T. & Pellikaan, G. R., 2000, In : Designs, Codes and Cryptography. 21, 1-3, p. 41-67

Research output: Contribution to journalArticleAcademicpeer-review

23 Citations (Scopus)
2 Downloads (Pure)
1999

On Weierstrass semigroups and the redundancy of improved geometric Goppa codes

Pellikaan, G. R. & Torres, F., 1999, In : IEEE Transactions on Information Theory. 45, 7, p. 2512-2519

Research output: Contribution to journalArticleAcademicpeer-review

15 Citations (Scopus)
1998

An elementary approach to algebraic geometry codes

Høholdt, T., van Lint, J. H. & Pellikaan, G. R., 1998, In : Congressus Numerantium. 135, p. 25-35

Research output: Contribution to journalArticlePopular

Generalized Hamming weights of q-ary Reed-Muller codes

Heijnen, P. W. & Pellikaan, G. R., 1998, In : IEEE Transactions on Information Theory. 44, 1, p. 181-196

Research output: Contribution to journalArticleAcademicpeer-review

64 Citations (Scopus)

Weierstrass semigroups in an asymptotically good tower of function fields

Pellikaan, G. R., Stichtenoth, H. & Torres, F., 1998, In : Finite Fields and their Applications. 4, 4, p. 381-392

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
22 Citations (Scopus)
1997

Blocking sets of almost Rédei type

Blokhuis, A., Pellikaan, G. R. & Szönyi, T., 1997, In : Journal of Combinatorial Theory, Series A. 78, 1, p. 141-150 10 p.

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)
1996

On the existence of error-correcting pairs

Pellikaan, G. R., 1996, In : Journal of Statistical Planning and Inference. 51, 2, p. 229-242 14 p.

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)
1995

On the decoding of algebraic-geometric codes

Høholdt, T. & Pellikaan, G. R., 1995, In : IEEE Transactions on Information Theory. 41, 6, p. 1589-1614

Research output: Contribution to journalArticleAcademicpeer-review

50 Citations (Scopus)

The minimum distance of codes in an array coming from telescopic semigroups

Kirfel, C. & Pellikaan, G. R., 1995, In : IEEE Transactions on Information Theory. 41, 6/1, p. 1720-1732

Research output: Contribution to journalArticleAcademicpeer-review

92 Citations (Scopus)
1993

Equality of geometric Goppa codes and equivalence of divisors

Munuera, C. & Pellikaan, G. R., 1993, In : Journal of Pure and Applied Algebra. 90, 3, p. 229-252

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
13 Citations (Scopus)
1992

Decoding geometric Goppa codes using an extra place

Porter, S. C., Shen, B. Z. & Pellikaan, G. R., 1992, In : IEEE Transactions on Information Theory. 38, 6, p. 1663-1676

Research output: Contribution to journalArticleAcademicpeer-review

35 Citations (Scopus)

On decoding by error location and dependent sets of error positions

Pellikaan, G. R., 1992, In : Discrete Mathematics. 106-107, 1, p. 369-381 13 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
41 Citations (Scopus)
1991

Which linear codes are algebraic-geometric?

Pellikaan, G. R., Shen, B. Z. & Wee, van, G. J. M., 1991, In : IEEE Transactions on Information Theory. 37, 3, p. 583-602

Research output: Contribution to journalArticleAcademicpeer-review

43 Citations (Scopus)
1990

Deformations of hypersurfaces with a one-dimensional singular locus

Pellikaan, G. R., 1990, In : Journal of Pure and Applied Algebra. 67, 1, p. 49-71 23 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
7 Citations (Scopus)
1989

Multiplicative structures on the minimal resolution of determinantal rings

Pellikaan, G. R., 1 Dec 1989, In : Indagationes Mathematicae. 51, 4, p. 471-478 8 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access

On a decoding algorithm for codes on maximal curves

Pellikaan, G. R., 1989, In : IEEE Transactions on Information Theory. 35, 6, p. 1228-1232

Research output: Contribution to journalArticleAcademicpeer-review

33 Citations (Scopus)

On hypersurface singularities which are stems

Pellikaan, G. R., 1989, In : Compositio Mathematica. 71, 2, p. 229-240 12 p.

Research output: Contribution to journalArticleAcademicpeer-review

1988

Finite determinacy of functions with non-isolated singularities

Pellikaan, G. R., 1988, In : Proceedings of the London Mathematical Society. Third series. 57, 2, p. 357-382 26 p.

Research output: Contribution to journalArticleAcademicpeer-review

35 Citations (Scopus)

Projective resolutions of the quotient of two ideals

Pellikaan, G. R., 1988, In : Indagationes Mathematicae (Proceedings). 91, 1, p. 65-84

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)