Constacyclic Codes over Finite Chain Rings of Characteristic p

被引:7
作者
Alabiad, Sami [1 ]
Alkhamees, Yousef [1 ]
机构
[1] King Saud Univ, Dept Math, Riyadh 11451, Saudi Arabia
关键词
finite ring; linear code; polynomials; coding theory; CYCLIC CODES; NEGACYCLIC CODES; LENGTH; Z(4);
D O I
10.3390/axioms10040303
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let R be a finite commutative chain ring of characteristic p with invariants p,r, and k. In this paper, we study lambda-constacyclic codes of an arbitrary length N over R, where lambda is a unit of R. We first reduce this to investigate constacyclic codes of length ps (N=n1ps, p does not divide 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 gamma between R[x]/ and a direct sum & OPLUS;b & ISIN;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 gamma so that the unique polynomial representations of lambda-constacyclic codes may be calculated. Finally, for k=2 the exact number of such codes is provided.
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页数:14
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