Constacyclic codes of length \(kl^{m}p^{n}\) over a finite field. (English) Zbl 1404.94149
Summary: We correct Theorem 1 and Theorem 3 in [H. Tong, Finite Fields Appl. 41, 159–173 (2016; Zbl 1372.94466)] and give the factorization of \(x^{k l^m p^n} - \lambda(\lambda \in \mathbb{F}_q^\ast)\) in the case that \(\gcd(k, q - 1) = 1\) and \(l |(q - 1)\). Then, for different odd primes \(k\), \(l\) and \(p\), the structures of constacyclic codes of length \(k l^m p^n\) over a finite field \(\mathbb{F}_q\) with characteristic \(p\) are obtained in terms of the generator polynomials completely.
MSC:
| 94B15 | Cyclic codes |
| 11T71 | Algebraic coding theory; cryptography (number-theoretic aspects) |
| 94B05 | Linear codes (general theory) |
Citations:
Zbl 1372.94466References:
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