Results 1 to 10 of about 374,736 (158)

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

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   +2 more sources

Self-Dual Codes [PDF]

, 2002
Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory. Topics covered in this survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight enumerators, Gleason-Pierce ...
Rains, E. M., Sloane, N. J. A.
core   +3 more sources

Symplectic QSD, LCD, and ACD Codes over a Non-Commutative Non-Unitary Ring of Order Nine [PDF]

Entropy
We introduce quasi self-dual (QSD), linear complementary dual (LCD), and additive complementary dual (ACD) codes for the symplectic inner product over a non-commutative non-unitary ring of order 9. We establish connections with symplectic–self-orthogonal
Sarra Manseri, Patrick Solé, Adel Alahmadi, Widyan Basaffar   +3 more
doaj   +2 more sources

On Quasi-Cyclic Codes of Index 3 [PDF]

Entropy
Quasi-cyclic codes of index 3 over finite fields are studied. We give a classification of such codes. Their duals with respect to the Euclidean and Hermitian inner products are investigated.
Kanat Abdukhalikov, Rasha M. Shat
doaj   +2 more sources

Ternary quantum codes constructed from extremal self-dual codes and self-orthogonal codes

AIMS Mathematics, 2022
In this paper, we consider S-chains of extremal self-dual and self-orthogonal codes and their applications in the construction of quantum codes. Then, by virtue of covering radius, we determine necessary conditions for linear codes to have subcodes with ...
Chaofeng Guan, Ruihu Li , Hao Song , Liangdong Lu, Husheng Li   +4 more
doaj   +1 more source

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 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

Self-Dual Codes, Symmetric Matrices, and Eigenvectors

IEEE Access, 2021
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ using symmetric matrices and eigenvectors from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$ . Using this method, which is called a
Jon-Lark Kim, Whan-Hyuk Choi
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

The mass formula for self-orthogonal and self-dual codes over a non-unitary commutative ring

AIMS Mathematics, 2023
In this paper, we establish a mass formula for self-orthogonal codes, quasi self-dual codes, and self-dual codes over commutative non-unital rings $ {{\mathit {I}_p}} = \left < a, b | pa = pb = 0, a^2 = b, ab = 0 \right > $, where $ p $ is an odd ...
Adel Alahmadi , Altaf Alshuhail, Patrick Solé   +2 more
doaj   +1 more source