通信学报2017，Vol.38Issue(2)：74-80,7.DOI:10.11959/j.issn.1000-436x.2017030
最小距离为4的最优五元循环码
Optimal quinary cyclic codes with minimum distance four
摘要
Abstract
Cyclic codes are an extremely important subclass of linear codes. They are widely used in the communication systems and data storage systems because they have efficient encoding and decoding algorithm. Until now, how to con-struct the optimal ternary cyclic codes has received a lot of attention and much progress has been made. However, there is less research about the optimal quinary cyclic codes. Firstly, an efficient method to determine if cyclic codesC(1,e,t) were optimal codes was obtained. Secondly, based on the proposed method, when the equatione=5k+1 ore=5m?2hold, the theorem that the cyclic codesC(1,e,t)were optimal quinary cyclic codes was proved. In addition, perfect nonlinear mo-nomials were used to construct optimal quinary cyclic codes with parameters[5m?1,5m?2m?2,4] optimal quinary cyclic codes overF5m.关键词
有限域/循环码/最小距离/完全非线性函数Key words
finite field/cyclic codes/minimum distance/perfect nonlinear function分类
信息技术与安全科学引用本文复制引用
田叶,张玉清,胡予濮..最小距离为4的最优五元循环码[J].通信学报,2017,38(2):74-80,7.基金项目
国家自然科学基金资助项目(No.61572460, No.61272481) （No.61572460, No.61272481）
国家重点研究计划基金资助项目(No.2016YFB0800703) （No.2016YFB0800703）
国家发展改革委员会信息安全专项基金资助项目(No.(2012)1424) （No.(2012）
高等学校学科创新引智计划("111"计划)基金资助项目(No.B16037)The National Natural Science Foundation of China (No.61572460, No.61272481), The National Key Research and Development Project (No.2016YFB0800703), The National Information Security Special Projects of National Development, the Reform Commission of China (No.(2012)1424), China 111 Project (No.B16037) （"111"计划）
