Several new classes of optimal p-ary cyclic codes

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≥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 Cₚ(0,s,t), which possess the parameters [pᵐ - 1,pᵐ - 2m - 2,4]. Here, s is defined as s = pᵐ+12, and t satisfies the condition 2 ≤ t ≤ pᵐ - 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 C₅(0,s,t).