2018/05/15 by Yuan Cao, Yonglin Cao, Cao, Yuan +9
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Cellular Automata and Applications
paper · pdf · doi:10.48550/arxiv.1805.05595
Let \mathbbFpm be a finite field of cardinality pm where p is an odd prime, n be a positive integer satisfying \rm gcd(n,p)=1, and denote R=\mathbbFpm[u]/⟨ ue⟩ where e≥ 4 be an even integer. Let δ,α∈ \mathbbFpm×. Then the class of (δ+αu2)-constacyclic codes over R is a significant subclass of constacyclic codes over R of Type 2. For any integer k≥ 1, an explicit representation and a complete description for all distinct (δ+αu2)-constacyclic codes over R of length npk and their dual codes are given. Moreover, formulas for the number of codewords in each code and the number of all such codes are provided respectively. In particular, all distinct (δ+αu2)-contacyclic codes over \mathbbFpm[u]/⟨ ue⟩ of length pk and their dual codes are presented precisely.