【摘要】 定义了环Zp[u]/(um-1)上一个Gray映射,使得该映射是Zp[u]/(um-1)到Zp的距离保持映射,通过该映射及环Zp[u]/(um-1)上的码生成矩阵,可得到Gray映射像下码的生成矩阵。最后,证明了码C是环Zp[u]/(um-1)上一个循环码的充分必要条件为它的Gray映射下的像是一个准循环码。更多还原

【Abstract】 A Gray map over Z_p/(u~m-1) is defined, and the Gray map is proven to be an isometry. Moreover, if G is a generator matrix of a code C over Z_p/(u~m-1),then a generator matrix of (C) can be obtained. A necessary and sufficient condition for the Gray image of quasi-cyclic code to be cyclic is given.更多还原