Binary cyclic codes with two primitive nonzeros  

作　　者：FENG Tao LEUNG KaHin XIANG Qing 

机构地区：[1]Department of Mathematical Sciences, Zhejiang University [2]Department of Mathematical Sciences, National University of Singapore [3]Department of Mathematical Sciences, University of Delaware

出　　处：《Science China Mathematics》2013年第7期1403-1412,共10页中国科学：数学（英文版）

基　　金：supported in part by Fundamental Research Fund for the Central Universities of China;Zhejiang Provincial Natural Science Foundation(Grant No.LQ12A01019);National Natural Science Foundation of China(Grant No.11201418);Research Fund for Doctoral Programs from the Ministry of Education of China(Grant No.20120101120089);supported in part by AcRF grant(Grant No.R-146-000-158-112)

摘　　要：In this paper, we make some progress towards a well-known conjecture on the minimum weights of binary cyclic codes with two primitive nonzeros. We also determine the Walsh spectrum of Tr(x d ) over F2m in the case where m = 2t, d = 3 + 2t+1 and gcd(d, 2m-1) = 1.In this paper, we make some progress towards a well-known conjecture on the minimum weights of binary cyclic codes with two primitive nonzeros. We also determine the Walsh spectrum of Tr（x^d） over F2m in the case where m = 2t, d = 3 ＋ 2^（t＋1） and gcd（d, 2m - 1） = 1.

关 键 词：cyclic code minimum weight Walsh spectrum 

分 类 号：O153.4[理学—数学]