两类具有两个零点的最优三元循环码

Two Classes of Optimal Ternary Cyclic Codes with Two Zeros

本文从生成多项式的角度研究具有两个零点的三元循环码。运用有限域上的多变元、因式分解和低次不可约多项式解的结构等数学知识,得到了两类参数为[ 3m−1,3m−2m−1,4 ]的三元循环码,并关于Sphere-Packing界是紧的。This paper studies ternary cyclic codes with two zeros from the perspective of generating polynomials. By employing mathematical knowledge such as multivariate polynomials over finite fields, factorization, and the structure of solutions for low-degree irreducible polynomials, we obtain two classes of ternary cyclic codes with parameters [ 3m−1,3m−2m−1,4 ]. These codes are shown to be tight with respect to the Sphere-Packing bound.