Recently, linear codes over finite fields with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. In this paper, for an o...Recently, linear codes over finite fields with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. In this paper, for an odd prime p,the complete weight enumerator of a class of p-ary linear codes based on defining sets are determined. Furthermore, from the explicit complete weight enumerator of linear codes, a new class of optimal constant composition codes and several classes of asymptotically optimal systematic authentication codes are obtained.展开更多
给出环n s(k)M上线性码的精确完全重量计数器的定义及相应的MacWilliams恒等式,并对环M n s(k)上线性码的精确完全重量计数器、k上线性码的精确重量计数器以及k上线性码的完全重量计数器之间的联系进行研究,结果表明,环M n s(k)上线性...给出环n s(k)M上线性码的精确完全重量计数器的定义及相应的MacWilliams恒等式,并对环M n s(k)上线性码的精确完全重量计数器、k上线性码的精确重量计数器以及k上线性码的完全重量计数器之间的联系进行研究,结果表明,环M n s(k)上线性码的精确完全重量计数器相比其他2种重量计数器更具一般性,可更好地用于码的结构研究和译码错误概率计算。展开更多
基金Research supported by the NSFC(11701317)China Postdoctoral Science Foundation Funded Project(2017M611801)the Open Project Program of the Key Lab of Informaltion Security,Guangzhou University(GDXXAQ2016-08)
基金supported by the National Natural Science Foundation of China under Grant No.11401408Project of Science and Technology Department of Sichuan Province under Grant No.2016JY0134the National Key R and Program of China under Grant No.2016QY04W080
文摘Recently, linear codes over finite fields with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. In this paper, for an odd prime p,the complete weight enumerator of a class of p-ary linear codes based on defining sets are determined. Furthermore, from the explicit complete weight enumerator of linear codes, a new class of optimal constant composition codes and several classes of asymptotically optimal systematic authentication codes are obtained.
文摘给出环n s(k)M上线性码的精确完全重量计数器的定义及相应的MacWilliams恒等式,并对环M n s(k)上线性码的精确完全重量计数器、k上线性码的精确重量计数器以及k上线性码的完全重量计数器之间的联系进行研究,结果表明,环M n s(k)上线性码的精确完全重量计数器相比其他2种重量计数器更具一般性,可更好地用于码的结构研究和译码错误概率计算。
