Results 31 to 40 of about 645,715 (278)

Triorthogonal codes and self-dual codes

Quantum Information Processing
21 ...
Minjia Shi, Haodong Lu, Jon-Lark Kim, Patrick Solé   +3 more
openaire   +2 more sources

PERSYMMETRIC MATRIX AND ITS APPLICATION IN CODING THEORY

Barekeng
A persymmetric matrix is a square matrix that is symmetric concerning its antidiagonal. This article discusses some characteristics of a persymmetric matrix and its application in coding theory. A persymmetric matrix is used to form a generator matrix of
Ardi Nur Hidayat, Vira Hari Krisnawati, Abdul Rouf Alghofari   +2 more
doaj   +1 more source

Duality of Codes Over Non-Unital Rings of Order Four

IEEE Access, 2023
In this paper, we present a basic theory of the duality of linear codes over three of the non-unital rings of order four; namely $I$ , $E$ , and $H$ as denoted in (Fine, 1993).
Adel Alahmadi, Asmaa Melaibari, Patrick Sole   +2 more
doaj   +1 more source

New extremal binary self-dual codes of length 68 from quadratic residue codes over f_2+uf_2+u^2f_2

, 2013
In this work, quadratic reside codes over the ring F2 +uF2 +u^2F2 with u^3 = u are considered. A duality and distance preserving Gray map from F2 + uF2 + u^2F2 to (F_2)^3 is defined.
Kaya, Abidin, Siap, Irfan, Yildiz, Bahattin   +2 more
core   +1 more source

Kneser-Hecke-operators in coding theory

, 2006
The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length.
Nebe, Gabriele
core   +2 more sources

Representing Small Identically Self‐Dual Matroids by Self‐Dual Codes [PDF]

SIAM Journal on Discrete Mathematics, 2006
The matroid associated with a linear code is the representable matroid that is defined by the columns of any generator matrix. The matroid associated with a self-dual code is identically self-dual, but it is not known whether every identically self-dual representable matroid can be represented by a self-dual code.
Carles Padró, Ignacio Gracia
openaire   +2 more sources

Reversible Self-Dual Codes Over the Ring F₂ + uF₂

IEEE Access
In this study, we introduce bisymmetric self-dual codes over the finite field ${\mathbb F}_{2}$ of order two. We developed a method to generate binary bisymmetric self-dual codes from a small-length bisymmetric self-dual code by increasing its length ...
Hyun Jin Kim, Whan-Hyuk Choi
doaj   +1 more source

An Enumeration of the Equivalence Classes of Self-Dual Matrix Codes

, 2015
As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, these codes have also been termed rank-metric codes, space-time codes over ...
Morrison, Katherine
core   +1 more source

Construction of isodual codes from polycirculant matrices

, 2020
Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual.
Shi, Minjia, Sole, Patrick, Xu, Li
core   +3 more sources

New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields

Entropy, 2019
Maximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality.
Aixian Zhang, Zhe Ji
doaj   +1 more source