摘要
在有限环F2+uF2+…+ukF2与F2之间定义一个新的Gray映射,证明了该映射是距离保持映射。考察了F2+uF2+…+ukF2环上循环码,得到了F2+uF2+…+ukF2环上循环码的生成多项式。最后,证明了F2+uF2+…+ukF2环上循环码在新定义的Gray映射下的像是F2上的准循环码。
A new Gray map was defined from F2+uF2+…+u^k F2 to F2, and the Gray map was proved to be isometry. Cyclic codes over F2+uF2+…+u^k F2 were studied, and the generator polynomials of cyclic codes were obtained. Moreover, the Gray map of cyclic codes is a quasi-cyclic codes over F2.
出处
《通信学报》
EI
CSCD
北大核心
2006年第9期86-88,共3页
Journal on Communications