摘要
讨论了非有限链环R=F_p+uF_p+vF_p+uvF_p上的循环码.通过环R上的循环码与多项式环R_n=(F_p+uF_p+vF_p+uvF_p)[x]/(x^n-1)的理想的对应关系及对R_n的研究给出了R上循环码的刻画.最后定义了一个Gray映射,并刻画了F_p+uF_p+vF_p+uvF_p上的循环码在该映射下的像.
In this paper, cyclic codes over the ring R = Fp --k uFp + VFp q- uvFp are discussed, where the ring R is not afinite chain ring. By studying the polynomial ring Rn=(Fp+uFp+vFp+uvFp)[x]/(xn=1) and using the corresponding relationship between the cyclic codes over the ring R and the ideals in the ringRn, cyclic codes over the ring R are characterized. Finally, a Gray-map is obtained and the images of cyclic codes over the ring R are characterized.
出处
《数学的实践与认识》
CSCD
北大核心
2013年第1期118-123,共6页
Mathematics in Practice and Theory
基金
湖北省教育厅科学技术研究项目(B20114410)
黄石理工学院自然科学类青年项目(11yjz31Q)