【摘 要】
：
众所周知,有限域上二次剩余码是一类特殊的循环码,有较大的最小距离.设g是正整数,m是大于1的正整数且p,p1,p2,…,pg为不同的奇质数.本文将有限域上码长为奇质数的二次剩余码的概念推广到码长为n=∏gi=1pi的二次剩余码和码长为p的m次剩余码,得到这些码是LCD码或自正交码的充要条件,并给出相应的计数公式.特别地,本文确定了所有24个四元二次剩余码[15,8]及二元二次剩余码[161,81]的最小距离.“,”It is well known that the quadratic residue co
【机 构】
：
四川师范大学数学科学学院,成都,四川,610068
论文部分内容阅读
众所周知,有限域上二次剩余码是一类特殊的循环码,有较大的最小距离.设g是正整数,m是大于1的正整数且p,p1,p2,…,pg为不同的奇质数.本文将有限域上码长为奇质数的二次剩余码的概念推广到码长为n=∏gi=1pi的二次剩余码和码长为p的m次剩余码,得到这些码是LCD码或自正交码的充要条件,并给出相应的计数公式.特别地,本文确定了所有24个四元二次剩余码[15,8]及二元二次剩余码[161,81]的最小距离.“,”It is well known that the quadratic residue code over finite fields is an inter-esting class of cyclic codes for its higher minimum distance.Let g be a positive integer and p,p1,p2,…,pg be distinct odd primes.The present paper generalizes the constructions for the quadratic residue code with length p to be the length n=∏gi=1pi,and to be the case m-th residue codes with length p over finite fields,where m≥2 is a positive integer.Furthermore,a criterion for that these codes are self-orthogonal or complementary dual is obtained,and then the corresponding counting formula is given.In particular,the minimum distances of all 24 quaternary quadratic residue codes[15,8]and all 24 binary quadratic residue codes[161,81]are determined.
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