On matrix-product structure of repeated-root constacyclic codes over finite fields
نویسندگان
چکیده
منابع مشابه
Matrix-product structure of repeated-root constacyclic codes over finite fields
For any prime number p, positive integers m, k, n satisfying gcd(p, n) = 1 and λ0 ∈ F × pm, we prove that any λ p 0 -constacyclic code of length p n over the finite field Fpm is monomially equivalent to a matrix-product code of a nested sequence of p λ0-constacyclic codes with length n over Fpm.
متن کاملConstacyclic codes over finite fields
An equivalence relation called isometry is introduced to classify constacyclic codes over a finite field; the polynomial generators of constacyclic codes of length lp are characterized, where p is the characteristic of the finite field and l is a prime different from p.
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In this paper we investigate the structure of repeated root constacyclic codes of length 2mp over Fps with a ≥ 1 and (m, p) = 1. We characterize the codes in terms of their generator polynomials. This provides simple conditions on the existence of self-dual negacyclic codes. Further, we gave cases where the constacyclic codes are equivalent to cyclic codes.
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Let Fq be a finite field with q = p , where p is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over Fq. The enumeration of such codes is investigated. We obtain all the self-dual negacyclic codes of length 2p over Fq, a ≥ 1. The construction of self-dual negacyclic codes of length 2bp over Fq is also provided, where gcd(2, b) = gcd(b, p) = 1 and a ≥ 1.
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For any different odd primes ` and p, structure of constacyclic codes of length 2`p over the finite field Fq of characteritic p and their duals is established in term of their generator polynomials. Among other results, the characterization and enumeration of all linear complimentary dual and self-dual constacylic codes of length 2`p are obtained.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2020
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.111768