On a Class of (δ+αu²)-Constacyclic Codes over F_q[u]/<u⁴>

Abstract

Let F_q be a finite field of cardinality q, R=F_q[u]/<u⁴>=F_q+uF_q+u²F_q+u³F_q (u⁴=0) which is a finite chain ring, and n be a positive integer satisfying gcd(q,n)=1. For any $\delta,\alpha\in \mathbb{F}_{q}^{\times}$, an explicit representation for all distinct (δ+αu²)-constacyclic codes over R of length n is given, and the dual code for each of these codes is determined. For the case of q=2^m and δ=1, all self-dual (1+αu²)-constacyclic codes over R of odd length n are provided.