All alpha plus mu beta-constacyclic codes of length np(s) over F-p(m) + uF(p)(m)

作者：Zhao, Wei; Tang, Xilin^*; Gu, Ze

来源：Finite Fields and Their Applications, 2018, 50: 1-16.

DOI：10.1016/j.ffa.2017.10.006

• Constacyclic code
• Dual code
• Self dual code
• Repeated-root code

Let F-p(m) be a finite field with cardinality p(m) and R = F-p(m) + uF(p)(m) with u(2) = 0. We aim to determine all alpha+mu beta-constacyclic codes of length np(s) over R, where alpha, beta is an element of F*(m)(p), n, s is an element of N+ and gcd(n, p) = 1. Let alpha(0) is an element of F*(m)(p) and alpha(ps)(0) = alpha. The residue ring R[x]/< x(nps)- alpha- mu beta > is a chain ring with the maximal ideal (x(n) - alpha(0)) in the case that x(n) - alpha(0) is irreducible in F-p(m) [x]. If x(n) - alpha(0) is reducible in F-p(m) [x], we give the explicit expressions of the ideals of R[x]/< x(nPs) - alpha - mu beta >. Besides, the number of codewords and the dual code of every alpha + mu beta-constacyclic code are provided.

• 出版日期2018-3
• 单位华南理工大学; 肇庆学院