Results 11 to 20 of about 529,213 (275)

On Reversibility and Self-Duality for Some Classes of Quasi-Cyclic Codes

IEEE Access, 2020
In this work, we study two classes of quasi-cyclic (QC) codes and examine how several properties can be combined into the codes of these classes. We start with the class of QC codes generated by diagonal generator polynomial matrices; a QC code in this ...
Ramy Taki Eldin, Hajime Matsui
doaj   +1 more source

Self-Dual and Complementary Dual Abelian Codes over Galois Rings [PDF]

, 2019
Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications.
Jitman, Somphong, Ling, San
core   +3 more sources

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

Self-Dual Double Circulant, Self-Dual Double Negacirculant and LCD Double Negacirculant Codes Over the Ring F_q[u,v]/<u² - u, v²-v, uv-vu>

IEEE Access, 2023
In this paper, we investigate self-dual double circulant, and self-dual and linear complementary dual (LCD) double negacirculant codes over a finite ring $R = \mathbb F_{q} + u \mathbb F_{q} + v \mathbb F_{q} + uv\mathbb F_{q}$ , where $u^{2}=u$ , $v^{
Hai Q. Dinh, Bhanu Pratap Yadav, Bac T. Nguyen, Ashish Kumar Upadhyay, Woraphon Yamaka   +4 more
doaj   +1 more source

On Symbol-Pair Distance of a Class of Constacyclic Codes of Length 3p^s over ${\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$

Axioms, 2023
Let p≠3 be any prime. In this paper, we compute symbol-pair distance of all γ-constacyclic codes of length 3ps over the finite commutative chain ring R=Fpm+uFpm, where γ is a unit of R which is not a cube in Fpm.
Hai Q. Dinh, Hiep L. Thi, Roengchai Tansuchat   +2 more
doaj   +1 more source

On Hamming Distance Distributions of Repeated-Root Cyclic Codes of Length 5p^s Over F_p ^m + uF_p ^m

IEEE Access, 2022
Let $p\not =5$ be any odd prime. Using the algebraic structures of all cyclic codes of length $5p^{s}$ over the finite commutative chain ring ${\mathcal{ R}}=\mathbb F_{p^{m}}+u\mathbb F_{p^{m}}$ , in this paper, the exact values of Hamming ...
Hai Q. Dinh, Bac T. Nguyen, Hiep L. Thi, Woraphon Yamaka   +3 more
doaj   +1 more source

An explicit construction of quantum codes from one-generator generalized quasi-cyclic codes [PDF]

MATEC Web of Conferences, 2021
In this paper, we take advantage of a class of one-generator generalized quasi-cyclic (GQC) codes of index 2 to construct quantum error-correcting codes.
Yao Yu, Ma Yuena, Li Husheng, Lv Jingjie
doaj   +1 more source

An Algorithm for Finding Self-Orthogonal and Self-Dual Codes Over Gaussian and Eisenstein Integer Residue Rings Via Chinese Remainder Theorem

IEEE Access, 2023
A code over Gaussian or Eisenstein integer residue ring is an additive group of vectors with entries in this integer residue ring which is closed under the action of constant multiplication by the Gaussian or Eisenstein integers. In this paper, we define
Hajime Matsui
doaj   +1 more source

Galois self-dual constacyclic codes [PDF]

Designs, Codes and Cryptography, 2016
Key words: Constacyclic code, Galois inner product, $q$-coset function, isometry, Galois self-dual ...
Fan, Yun, Zhang, Liang
openaire   +2 more sources

New extremal singly even self-dual codes of lengths $64$ and $66$ [PDF]

, 2017
For lengths $64$ and $66$, we construct extremal singly even self-dual codes with weight enumerators for which no extremal singly even self-dual codes were previously known to exist. We also construct new $40$ inequivalent extremal doubly even self-dual $
Anev, Damyan, Harada, Masaaki, Yankov, Nikolay   +2 more
core   +3 more sources