Some Results on Cyclic Codes Over ${F}_{2}+v{F}_{2}$

作者：Shixin Zhu, Yu Wang, Minjia Shi · 发表于：IEEE Transactions on Information Theory · 年份：2010 · DOI：10.1109/tit.2010.2040896 · 被引用次数：85 · 研究领域：Coding theory and cryptography、graph theory and CDMA systems、Cellular Automata and Applications

In this paper, we investigate the structure and properties of cyclic codes over the ringF2+vF2. We first study the relationship between cyclic codes overF2+vF2and binary cyclic codes. Then we prove that cyclic codes over the ring are principally generated, and give the generator polynomial of cyclic codes over the ring. Finally, we obtain the unique idempotent generators for cyclic codes of odd length and determine the number of cyclic codes for a given lengthnoverF2+vF2.