一类新的最优三元循环码

A new class of optimal ternary cyclic codes

循环码是线性码的一个重要子类,由于代数结构清晰、编译码简单且易于实现,被广泛地应用于数据存储系统和通信系统中。本文研究了一类三元循环码,通过分析某些方程在三元域上的解,确定了此类三元循环码的参数,由Sphere Packing界证明了该码具有最优性。

Cyclic codes are an important subclass of linear codes.They are widely used in data storage systems and communication systems,because they have clear algebraic structure,simple encoding and decoding algorithms,and easy implementation.In this paper,a class of ternary cyclic codes is studied.By analyzing the solutions of some equations,the parameters of such ternary cyclic codes are determined.The optimality of the codes is proved by the Sphere Packing bound.