scholarly journals Repeated-root constacyclic codes of prime power lengths over finite chain rings

2017 ◽  
Vol 43 ◽  
pp. 22-41 ◽  
Author(s):  
Hai Q. Dinh ◽  
Hien D.T. Nguyen ◽  
Songsak Sriboonchitta ◽  
Thang M. Vo
Keyword(s):  
Prime Power ◽  
Constacyclic Codes ◽  
Finite Chain ◽  
Finite Chain Rings

scholarly journals Constacyclic Codes over Finite Chain Rings of Characteristic p

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 303
Author(s):  
Sami Alabiad ◽  
Yousef Alkhamees
Keyword(s):  
Local Rings ◽  
Constacyclic Codes ◽  
Finite Chain ◽  
Dual Codes ◽  
Chain Ring ◽  
Characteristic P ◽  
Arbitrary Length ◽  
Cyclotomic Cosets ◽  
Finite Chain Rings ◽  
Polynomial Representations

Let R be a finite commutative chain ring of characteristic p with invariants p,r, and k. In this paper, we study λ-constacyclic codes of an arbitrary length N over R, where λ is a unit of R. We first reduce this to investigate constacyclic codes of length ps (N=n1ps,p∤n1) over a certain finite chain ring CR(uk,rb) of characteristic p, which is an extension of R. Then we use discrete Fourier transform (DFT) to construct an isomorphism γ between R[x]/<xN−λ> and a direct sum ⊕b∈IS(rb) of certain local rings, where I is the complete set of representatives of p-cyclotomic cosets modulo n1. By this isomorphism, all codes over R and their dual codes are obtained from the ideals of S(rb). In addition, we determine explicitly the inverse of γ so that the unique polynomial representations of λ-constacyclic codes may be calculated. Finally, for k=2 the exact number of such codes is provided.

On the depth spectrum of repeated-root constacyclic codes over finite chain rings

2020 ◽  
Vol 343 (2) ◽  
pp. 111647
Author(s):  
Jian Yuan ◽  
Shixin Zhu ◽  
Xiaoshan Kai
Keyword(s):  
Constacyclic Codes ◽  
Finite Chain ◽  
Finite Chain Rings

A class of linear codes of length 2 over finite chain rings

2019 ◽  
Vol 19 (06) ◽  
pp. 2050103 ◽  
Author(s):  
Yonglin Cao ◽  
Yuan Cao ◽  
Hai Q. Dinh ◽  
Fang-Wei Fu ◽  
Jian Gao ◽  
...  
Keyword(s):  
Positive Integer ◽  
Linear Codes ◽  
Invertible Element ◽  
Irreducible Polynomial ◽  
Constacyclic Codes ◽  
Finite Chain ◽  
Chain Ring ◽  
Finite Chain Ring ◽  
Finite Chain Rings ◽  
Positive Integers

Let [Formula: see text] be a finite field of cardinality [Formula: see text], where [Formula: see text] is an odd prime, [Formula: see text] be positive integers satisfying [Formula: see text], and denote [Formula: see text], where [Formula: see text] is an irreducible polynomial in [Formula: see text]. In this note, for any fixed invertible element [Formula: see text], we present all distinct linear codes [Formula: see text] over [Formula: see text] of length [Formula: see text] satisfying the condition: [Formula: see text] for all [Formula: see text]. This conclusion can be used to determine the structure of [Formula: see text]-constacyclic codes over the finite chain ring [Formula: see text] of length [Formula: see text] for any positive integer [Formula: see text] satisfying [Formula: see text].

scholarly journals Skew Constacyclic Codes over Finite Fields and Finite Chain Rings

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Hai Q. Dinh ◽  
Bac T. Nguyen ◽  
Songsak Sriboonchitta
Keyword(s):  
Finite Fields ◽  
Bch Codes ◽  
Constacyclic Codes ◽  
Finite Chain ◽  
Dual Codes ◽  
Negacyclic Codes ◽  
Finite Chain Rings

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 overFpm+uFpmin particular. Moreover, general decoding procedure for decoding skew BCH codes with designed distance and an algorithm for decoding skew BCH codes are discussed.

scholarly journals Some constacyclic codes over finite chain rings

2016 ◽  
Vol 10 (4) ◽  
pp. 683-694 ◽  
Author(s):  
Aicha Batoul ◽  
Kenza Guenda ◽  
T. Aaron Gulliver
Keyword(s):  
Constacyclic Codes ◽  
Finite Chain ◽  
Finite Chain Rings

scholarly journals The depth spectrums of constacyclic codes over finite chain rings

2015 ◽  
Vol 338 (2) ◽  
pp. 256-261 ◽  
Author(s):  
Bo Kong ◽  
Xiying Zheng ◽  
Hongjuan Ma
Keyword(s):  
Constacyclic Codes ◽  
Finite Chain ◽  
Finite Chain Rings

scholarly journals Skew constacyclic codes over finite chain rings

2012 ◽  
Vol 6 (1) ◽  
pp. 39-63 ◽  
Author(s):  
Patanee Udomkavanich ◽  
San Ling ◽  
Somphong Jitman
Keyword(s):  
Constacyclic Codes ◽  
Finite Chain ◽  
Finite Chain Rings
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