A class of repeated-root constacyclic codes over F_p^m[u]/〈 u^e〉 of Type 2

05/15/2018

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by   Yuan Cao, et al.

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Let F_p^m be a finite field of cardinality p^m where p is an odd prime, n be a positive integer satisfying gcd(n,p)=1, and denote R=F_p^m[u]/〈 u^e〉 where e≥ 4 be an even integer. Let δ,α∈F_p^m^×. Then the class of (δ+α u^2)-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+α u^2)-constacyclic codes over R of length np^k 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+α u^2)-contacyclic codes over F_p^m[u]/〈 u^e〉 of length p^k and their dual codes are presented precisely.