Zobrazeno 1 - 10
of 85
pro vyhledávání: '"Pellikaan, Ruud"'
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 codes starting from the colorings of a knot, describing through a serie
Externí odkaz:
http://arxiv.org/abs/2307.14882
The extended coset leader weight enumerator of the generalized Reed-Solomon $[q + 1, q - 3, 5]_q$ code is computed. The computation is considered as a question in finite geometry. For this we need the classification of the points, lines and planes in
Externí odkaz:
http://arxiv.org/abs/2103.16904
Autor:
Pereira, Francisco Revson F., Pellikaan, Ruud, La Guardia, Giuliano Gadioli, de Assis, Francisco Marcos
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 parameters of these codes. For example, entanglement can provide a way for quan
Externí odkaz:
http://arxiv.org/abs/1907.06357
Autor:
Pellikaan, Ruud
Publikováno v:
IEEE Transactions on Information Theory, vol. 64 (4), pp. 3010-3017, 2018
The hull $H(C)$ of a linear code $C$ is defined by $H(C)=C \cap C^\perp$. A linear code with a complementary dual (LCD) is a linear code with $H(C)=\{0\}$. The dimension of the hull of a code is an invariant under permutation equivalence. For binary
Externí odkaz:
http://arxiv.org/abs/1707.08856
Autor:
Yardi, Arti, Pellikaan, Ruud
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 literature that some families of cyclic codes such as BCH codes and Reed-Sol
Externí odkaz:
http://arxiv.org/abs/1705.09859
Autor:
Jurrius, Relinde, Pellikaan, Ruud
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 they are (not) cryptomorphic. Also, we explain the motivation for stu
Externí odkaz:
http://arxiv.org/abs/1610.09250
Error-correcting pairs were introduced independently by Pellikaan and K\"otter as a general method of decoding linear codes with respect to the Hamming metric using coordinatewise products of vectors, and are used for many well-known families of code
Externí odkaz:
http://arxiv.org/abs/1512.08144
Error-correcting pairs were introduced in 1988 by R. Pellikaan, and were found independently by R. K\"otter (1992), as a general algebraic method of decoding linear codes. These pairs exist for several classes of codes. However little or no study has
Externí odkaz:
http://arxiv.org/abs/1508.02187
Autor:
Jurrius, Relinde, Pellikaan, Ruud
Publikováno v:
Advances in Mathematics of Communications, 11(1), 225-235, 2017
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 $L$, where $L$ is a finite Galois extension of a field $K$. This is a generalizati
Externí odkaz:
http://arxiv.org/abs/1506.02865
Publikováno v:
CIM-MS Series by Springer-Verlag (2014)
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 of such codes from random codes using the Schur product. Wieschebrink t
Externí odkaz:
http://arxiv.org/abs/1409.8220