Matrix-product structure of constacyclic codes over finite chain rings $\mathbb{F}_{p^m}[u]/\langle u^e\rangle$
نویسندگان
چکیده
Let m, e be positive integers, p a prime number, Fpm be a finite field of p elements and R = Fpm [u]/〈u 〉 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+ωu)-constacyclic code of length pn over R is monomially equivalent to a matrix-product code of a nested sequence of p cyclic codes with length n over R and a p × p matrix Apk over Fp. Using the matrix-product structures, we give an iterative construction of every (1+ωu)-constacyclic code by (1+ωu)constacyclic codes of shorter lengths over R.
منابع مشابه
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