A class of binary cyclic codes with five weights  

作　　者：LI ChunLei 1 , ZENG XiangYong 1, & HU Lei 2 1 Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, China 2 The State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100049, China 

出　　处：《Science China Mathematics》2010年第12期3279-3286,共8页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos. 60973130, 60773134, 10990011);National Basic Research (973) Program of China (Grant No.2007CB311201);supported by Natural Science Foundation for Excellent Youth Scholars of Hubei Province of China (Grant No. 2009CDA147)

摘　　要：In this paper, the dual code of the binary cyclic code of length 2 n-1 with three zeros α, α t 1 and α t 2 is proven to have five nonzero Hamming weights in the case that n 4 is even and t1 = 2 n/2 + 1, t2 = 2 n-1-2 n/2+1 + 1 or 2 n/2 + 3, where α is a primitive element of the finite field F 2 n . The dual code is a divisible code of level n/2+1, and its weight distribution is also completely determined. When n = 4, the dual code satisfies Ward's bound.In this paper, the dual code of the binary cyclic code of length 2 n-1 with three zeros α, α t 1 and α t 2 is proven to have five nonzero Hamming weights in the case that n 4 is even and t1 = 2 n/2 + 1, t2 = 2 n-1-2 n/2+1 + 1 or 2 n/2 + 3, where α is a primitive element of the finite field F 2 n . The dual code is a divisible code of level n/2+1, and its weight distribution is also completely determined. When n = 4, the dual code satisfies Ward’s bound.

关 键 词：cyclic code Niho EXPONENT EXPONENTIAL SUM Pless power MOMENT IDENTITY weight distribution 

分 类 号：O157.4[理学—数学]