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On the weight distributions of a class of cyclic codes

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成果类型:
期刊论文
作者:
Liu, Hongwei*;Wang, Xiaoqiang;Zheng, Dabin
通讯作者:
Liu, Hongwei
作者机构:
[Liu, Hongwei; Wang, Xiaoqiang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
[Zheng, Dabin] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Hubei, Peoples R China.
通讯机构:
[Liu, Hongwei] C
Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
语种:
英文
关键词:
Cyclic code;Weight distribution;Exponential sum;Quadratic form
期刊:
Discrete Mathematics
ISSN:
0012-365X
年:
2018
卷:
341
期:
3
页码:
759-771
基金类别:
The authors would like to sincerely thank the Associate Editor and the anonymous referees for their helpful comments and suggestions, which have improved the presentation of this paper. The first author was supported by NSFC (Grant No. 11171370 ).
机构署名:
本校为第一且通讯机构
院系归属:
数学与统计学学院
摘要:
Let m and k be two positive integers such that v(2)(m) = v(2)(k), where v(2)(.) denotes the 2-valuation function, and let alpha be a primitive element of F-p2m. Let C be a cyclic code over F-p with a parity-check polynomial h(1)(X)h(2)(X)h(3)(X) is an element of F-p2m [x], where h(1)(x), h(2)(x) and h(3)(x) are the minimal polynomials of alpha(-pk+1/2), -alpha(-pk+1/2) and alpha(-pm+1/2) over F-p respectively. In this paper, we determine the weight distribution and the complete weight distributio...

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