一类Duadic群代数码的存在性

Existence of a Class of Duadic Group Algebra Codes

Ｄｕａｄｉｃ码是群代数ＧＦ（ｑ）Ｇ中满足一些条件的幂等元生成的左理想，其中Ｇ是有限群且（ｑ，｜Ｇ｜）＝１．考虑ｑ＝２，Ｇ为ｍｎ阶非阿贝尔群（其中ｍ，ｎ是奇素数）且劈分为μ－１的ｄｕａｄｉｃ码存在的充分条件和必要条件．

Duadic codes are defined in terms of idempotents of a group algebra GF(q)G ,where G is a finite group and gcd (q,|G|)=1.Under the conditions of q=2, G is a finite group of order mn ,where both m and n are odd prime numbers, the splitting is μ -1 , the necessary condition and sufficieat condition for the existence of such duadic codes are presented.