Several new classes of optimal p-ary cyclic codes

Abstract

Cyclic codes, as a crucial subclass of linear codes, exhibit broad applications in communication systems, data storage systems, and consumer electronics, primarily attributed to their well-structured algebraic properties. Let $p$ denote an odd prime with $p\ge 5$, and let $m$ be a positive integer. The primary objective of this paper is to construct three novel classes of optimal $p$-ary cyclic codes, denoted as ${\mathcal{C}}_p(0,s,t)$, which possess the parameters $[p^m-1,p^m-2m-2,4]$. Here, $s$ is defined as $s=\frac{p^m+1}{2}$, and $t$ satisfies the condition $2\le t\le p^m-2$. Notably, one of the constructed classes includes certain known optimal quinary cyclic codes as special cases. Furthermore, for the specific case when $p=5$, this paper additionally presents four new classes of optimal cyclic codes ${\mathcal{C}}_5(0,s,t)$.