The weight distribution of some irreducible cyclic codes

被引：32
|
作者：
Sharma, Anuradha [1 ]
Bakshi, Gurmeet K. [2 ]
机构：
[1] Indian Inst Technol Delhi, Dept Math, New Delhi 110016, India
[2] Panjab Univ, Ctr Adv Study Math, Chandigarh 160014, India
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2012年 / 18卷 / 01期
关键词：
Irreducible cyclic codes; Cyclotomic cosets; Weight distribution; GAUSS SUMS;
D O I：
10.1016/j.ffa.2011.07.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let F(q) be the finite field with q elements, p be an odd prime co-prime to q and m >= 1 be an integer. In this paper, we explicitly determine the weight distribution of all the irreducible cyclic codes of length p(m) over F(q) from their generating polynomials in three different cases, when (i) the multiplicative order of q modulo p(m) is phi(p(m)), (ii) the multiplicative order of q modulo p(m) is a power of p, and (iii) the multiplicative order of q modulo p(m) is twice a power of p. (C) 2011 Elsevier Inc. All rights reserved.
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页码：144 / 159
页数：16
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