On LCD repeated-root cyclic codes over finite fields

Abstract

In this paper, we investigate the LCD repeated-root cyclic codes of length \(n=n'p^r\) over the finite field \(\mathbb {F}_q\), where gcd\((n',p)=1\). We give a necessary and sufficient condition for a repeated-root cyclic code to be LCD over \(\mathbb {F}_q\). We also determine the minimum distance of LCD repeated-root cyclic codes over \(\mathbb {F}_q\). Finally, we give the enumeration of LCD repeated-root cyclic codes of length n over \(\mathbb {F}_q\).