Results 11 to 20 of about 226,788 (288)

Determinants of tridiagonal matrices over some commutative finite chain rings

Special Matrices
Diagonal matrices and their generalization in terms of tridiagonal matrices have been of interest due to their nice algebraic properties and wide applications.
Jitman Somphong, Sricharoen Yosita
doaj   +2 more sources

Skew Constacyclic Codes over Finite Fields and Finite Chain Rings [PDF]

Mathematical Problems in Engineering, 2016
This paper overviews the study of skewΘ-λ-constacyclic codes over finite fields and finite commutative chain rings. The structure of skewΘ-λ-constacyclic codes and their duals are provided. Among other results, we also consider the Euclidean and Hermitian dual codes of skewΘ-cyclic and skewΘ-negacyclic codes over finite chain rings in general and ...
Dinh, Hai Q., Nguyen, Bac T., Sriboonchitta, Songsak   +2 more
semanticscholar   +4 more sources

On cyclic codes over finite chain rings

Journal of Physics: Conference Series, 2021
Abstract Recent studies involve various approaches to establish a generating set for cyclic codes of arbitrary length over the class of Galois rings. One such approach involves the use of polynomials with minimal degree corresponding to specific subsets of the code, defined progressively.
null Monika, Sucheta Dutt, Ranjeet Sehmi
openaire   +2 more sources

Primitive idempotents and constacyclic codes over finite chain rings [PDF]

Gulf Journal of Mathematics, 2020
Let R be a commutative local finite ring. In this paper, we construct the complete set of pairwise orthogonal primitive idempotents of R[X]/ <g> where g is a regular polynomial in R[X]. We use this set to decompose the ring R[X]/ <g> and to give the structure of constacyclic codes over finite chain rings.
Charkani, Mohammed Elhassani, Kabore, Joël   +1 more
openaire   +3 more sources

$G$-codes over formal power series rings and finite chain rings

Journal of Algebra Combinatorics Discrete Structures and Applications, 2020
In this work, we define $G$-codes over the infinite ring $R_\infty$ as ideals in the group ring $R_\infty G$. We show that the dual of a $G$-code is again a $G$-code in this setting. We study the projections and lifts of $G$-codes over the finite chain rings and over the formal power series rings respectively.
Steven T. DOUGHERTY, Joe GİLDEA, Adrian KORBAN   +2 more
openaire   +6 more sources

Linear complementary pair of group codes over finite chain rings [PDF]

Designs, Codes and Cryptography, 2020
Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their applications in cryptography, in the context of side-channel and fault injection attacks. The security parameter for an LCP of codes $(C,D)$ is defined as the minimum of the minimum distances $d(C ...
Cem Güneri, Edgar Martínez-Moro, Selcen Sayıcı   +2 more
openaire   +6 more sources

LCD codes over finite chain rings

Finite Fields and Their Applications, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xiusheng, Liu, Hualu
openaire   +2 more sources

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   +2 more sources

Quantum codes from linear codes over finite chain rings [PDF]

Quantum Information Processing, 2017
In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to self-dual codes over finite chain rings. The second construction is derived from the CSS construction applied to Gray images of the linear codes over finite
Liu, Xiusheng, Liu, Hualu
openaire   +4 more sources

MDS and MHDR Cyclic Codes over Finite Chain Rings

Journal of Mathematics
This work establishes a unique set of generators for a cyclic code over a finite chain ring. Towards this, we first determine the minimal spanning set and rank of the code.
Monika Dalal, Sucheta Dutt, Ranjeet Sehmi   +2 more
doaj   +3 more sources