Repeated-root constacyclic codes of length kslmpn over finite fields

Abstract

For different odd primes k, l, p, and positive integers s, m, n, the polynomial $x^{k^s{l}^m{p}^n}-\lambda$ in $F_q\left[x\right]$ is explicitly factorized, where p is the characteristic of $F_q$, $\lambda \in F_q^{⁎}$. All repeated-root constacyclic codes and their dual codes of length $k^s{l}^m{p}^n$ over $F_q$ are characterized. In addition, the characterization and enumeration of all linear complementary dual (LCD) cyclic and negacyclic codes of length $k^s{l}^m{p}^n$ over $F_q$ are obtained.