摘要
在信息理论中,最优线性码具有很强的纠错能力、低相关性线性序列在密码系统和CDMA通信系统中得到了广泛应用.因此构造最优线性码和构造低相关性线性序列具有重要的研究价值.记R=Fp+uFp,这里的p为奇素数.本文首先通过迹映射构造出环R上的一类新的线性码,然后将这类新的线性码的删余码通过Gray映射得到了域Fp上一类最优码.同时,通过迹映射构造出环R上的一类线性循环码,将这类线性循环码视为线性周期序列并通过广义Nechaev-Gray映射得到了域Fp上一类低相关线性周期序列.
In information theory, optimal linear codes have good capability in error-correcting in coding theory and linear se- quences with low correlation have been widely used in cryptography and CDMA systems. Therefore, it has great value to study the conslruction of optimal linear codes and low correlation linear sequences. Let R = Fp ＋ uFp, where p is an odd prime. A class of new linear codes over R is constructed by means of the/race map. Then a kind of optimal codes over Fp is obtained via the Gray map from the punctured new linear codes. Furthermore, a class of new linear cyclic codes over R is also constructed by means of the trace map. A kind of low correlation linear sequences over Fp is observed via the generalized Nechaev-Gray map from the class of new linear cyclic codes, which are regarded as a class of linear periodic sequences.
出处
《电子学报》
EI
CAS
CSCD
北大核心
2014年第3期572-577,共6页
Acta Electronica Sinica
基金
安徽省自然科学基金(No.1208085MA14
No.1408085QF116)
安徽省高校省级科学研究项目(No.KJ2013B217
No.KJ2013B220
No.KJ2013B221)
合肥师范学院一般研究项目(No.2012kj10)
国家自然科学基金(No.61370089)
关键词
迹映射
最优线性码
低相关性
线性序列
trace map
optimal linear codes
low correlation
linear sequences
