Matrix-product structure of constacyclic codes over finite chain rings F_p^m[u]/〈 u^e〉

03/03/2018

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by   Yuan Cao, et al.

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Let m,e be positive integers, p a prime number, F_p^m be a finite field of p^m elements and R=F_p^m[u]/〈 u^e〉 which is a finite chain ring. For any ω∈ R^× and positive integers k, n satisfying gcd(p,n)=1, we prove that any (1+ω u)-constacyclic code of length p^kn over R is monomially equivalent to a matrix-product code of a nested sequence of p^k cyclic codes with length n over R and a p^k× p^k matrix A_p^k over F_p. Using the matrix-product structures, we give an iterative construction of every (1+ω u)-constacyclic code by (1+ω u)-constacyclic codes of shorter lengths over R.