Results 41 to 50 of about 4,270,277 (317)

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

Skew Cyclic Codes Over ℤ₄ + uℤ₄ With Derivation Based on a New Gray Map and Automorphism

IEEE Access
This paper investigates the algebraic structure and properties of skew cyclic codes over the finite chain ring $R = \mathbb {Z}_{4} + u\mathbb {Z}_{4}$ , where $u^{2} = 0$ .
Eda Tekin
doaj   +1 more source

Quantum codes from $ \sigma $-dual-containing constacyclic codes over $ \mathfrak{R}_{l, k} $

AIMS Mathematics, 2023
Let $ \mathfrak{R}_{l, k} = {\mathbb F}_{p^m}[u_1, u_2, \cdots, u_k]/ \langle u_{i}^{l} = u_{i}, u_iu_j = u_ju_i = 0 \rangle $, where $ p $ is a prime, $ l $ is a positive integer, $ (l-1)\mid(p-1) $ and $ 1\leq i, j\leq k $. First, we define a Gray map $
Xiying Zheng, Bo Kong, Yao Yu
doaj   +1 more source

Application of Constacyclic codes to Quantum MDS Codes

, 2014
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian construction ...
Chen, Bocong, Ling, San, Zhang, Guanghui
core   +1 more source

γ-Dual Codes over Finite Commutative Chain Rings

Axioms
In this article, the notion of γ-dual codes over finite chain rings is introduced as an extension of dual codes over finite chain rings. Various characteristics and properties of γ-dual codes over finite chain rings are explored.
Hai Q. Dinh, Hiep L. Thi, Roengchai Tansuchat   +2 more
doaj   +1 more source

Graph-Based Classification of Self-Dual Additive Codes over Finite Fields

, 2008
Quantum stabilizer states over GF(m) can be represented as self-dual additive codes over GF(m^2). These codes can be represented as weighted graphs, and orbits of graphs under the generalized local complementation operation correspond to equivalence ...
Danielsen, Lars Eirik
core   +4 more sources

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

Triorthogonal codes and self-dual codes

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

Skew Convolutional Codes

Entropy, 2020
A new class of convolutional codes, called skew convolutional codes, that extends the class of classical fixed convolutional codes, is proposed.
Vladimir Sidorenko, Wenhui Li, Onur Günlü, Gerhard Kramer   +3 more
doaj   +1 more source

New MDS Euclidean and Hermitian self-dual codes over finite fields [PDF]

arXiv.org, 2016
In this paper, we construct MDS Euclidean self-dual codes which are extended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic ...
Hongxi Tong, Xiaoqing Wang
semanticscholar   +1 more source