224 citations · 293 across the 12 of their papers we have counts for
13 papers
A New Invariant for Prime Alternating Knots From Error-Correcting Codes
Altan B. Kilic, Ruud Pellikaan, Alberto Ravagnan
This paper shows that the Alexander-Briggs code of a knot gives rise to a new invariant that distinguishes prime alternating knots. The restriction to prime alternating knots preci…
Knot Theory and Error-Correcting Codes
Altan B. Kilic, Anne Nijsten, Ruud Pellikaan +1
This paper builds a novel bridge between algebraic coding theory and mathematical knot theory, with applications in both directions. We give methods to construct error-correcting c…
The extended coset leader weight enumerator of a twisted cubic code
Aart Blokhuis, Ruud Pellikaan, Tamás Szőnyi
The extended coset leader weight enumerator of the generalized Reed-Solomon code is computed. The computation is considered as a question in finite geometry.…
Entanglement-assisted Quantum Codes from Algebraic Geometry Codes
Francisco Revson F. Pereira, Ruud Pellikaan, Giuliano Gadioli La Guardia +1
Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameter…
LCD codes over are as good as linear codes for q at least four
Ruud Pellikaan
The hull of a linear code is defined by . A linear code with a complementary dual (LCD) is a linear code with . The dimension of the hul…
On shortened and punctured cyclic codes
Arti Yardi, Ruud Pellikaan
The problem of identifying whether the family of cyclic codes is asymptotically good or not is a long-standing open problem in the field of coding theory. It is known in the litera…
Defining the q-analogue of a matroid
Relinde Jurrius, Ruud Pellikaan
This paper defines the q-analogue of a matroid and establishes several properties like duality, restriction and contraction. We discuss possible ways to define a q-matroid, and why…
Rank error-correcting pairs
Umberto Martínez-Peñas, Ruud Pellikaan
Error-correcting pairs were introduced independently by Pellikaan and Kötter as a general method of decoding linear codes with respect to the Hamming metric using coordinatewise pr…
A characterization of MDS codes that have an error correcting pair
Irene Márquez-Corbella, Ruud Pellikaan
Error-correcting pairs were introduced in 1988 by R. Pellikaan, and were found independently by R. Kötter (1992), as a general algebraic method of decoding linear codes. These pair…
On defining generalized rank weights
Relinde Jurrius, Ruud Pellikaan
This paper investigates the generalized rank weights, with a definition implied by the study of the generalized rank weight enumerator. We study rank metric codes over , where $…
Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes
Alain Couvreur, Irene Márquez-Corbella, Ruud Pellikaan
We give a polynomial time attack on the McEliece public key cryptosystem based on subcodes of algebraic geometry (AG) codes. The proposed attack reposes on the distinguishability o…
Cryptanalysis of McEliece Cryptosystem Based on Algebraic Geometry Codes and their subcodes
Alain Couvreur, Irene Márquez-Corbella, Ruud Pellikaan
We give polynomial time attacks on the McEliece public key cryptosystem based either on algebraic geometry (AG) codes or on small codimensional subcodes of AG codes. These attacks…
Error-correcting pairs for a public-key cryptosystem
Irene Márquez-Corbella, Ruud Pellikaan
Code-based cryptography is an interesting alternative to classic number-theory PKC since it is conjectured to be secure against quantum computer attacks. Many families of codes hav…