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 whe...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.展开更多
基金supported in part by Fundamental Research Fund for the Central Universities of ChinaZhejiang Provincial Natural Science Foundation(Grant No.LQ12A01019)+2 种基金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)
文摘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.
