非交换群上的Duadic码

Duadic Codes on Nonabelian Groups

p为奇素数,G为p^n阶非交换群.q与p互素.G有剖分的充分必要条件是μ-1是有限域GF(p)的一个剖分.当q=2,K=GF(2)时.若p≡-1(mod8).则群代数KG有Duadic码存在.

p is an odd prime,G is a nonabelian group of order pn ((q,p) = 1. There exists a splitting of G if and only if μ-1is a splitting of GF(p). There exist Duadic codes in the group algebra KG when q = 2,K = GF(2) and p=-1(mod8).