一类三元极小线性码的构造

Construction of a Class of Ternary Minimal Linear Codes

极小线性码作为一类特殊的线性码,在秘密共享方案、安全多方计算等方面有着重要应用,因此构造有限域上极小线性码有着重要意义。本文基于指数和、Krawtchouk多项式和F3m中定义在特殊向量集上的函数,构造了一类新的不满足Ashikhmin-Barg条件的三元极小线性码,并确定了它们的重量分布和完全重量计数。

Minimal linear codes,as a special category of linear codes,are critically important in applications such as secret sharing schemes and secure multi-party computation.It is of great significance to construct minimal linear codes over finite fields.Based on exponential sum,Krawtchouk polynomials and functions defined on special vector sets,we construct a new class of ternary minimal linear codes that do not satisfy the Ashikhmin-Barg condition,and then determine their weight distribution and complete weight enumerator.