关于一类hyperoval码的子域码的重量分布

兰州理工大学学报 ›› 2025, Vol. 51 ›› Issue (5): 167-172.

• 数理科学 • 上一篇

关于一类hyperoval码的子域码的重量分布

程卫东^*, 程文浩

重庆邮电大学理学院, 重庆 400065

收稿日期:2023-06-30 出版日期:2025-10-28 发布日期:2025-10-25
通讯作者: 程卫东(1984-),男,重庆云阳人,博士,讲师. Email:chengwd@cqupt.edu.cn
基金资助:
重庆市自然科学基金面上项目(CSTC2021JCYJ- MSXMX0575,CSTB2025NSCQ-GPX1287)

On weight distribution of a class of subfield codes of hyperoval codes

CHENG Wei-dong, CHENG Wen-hao

School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received:2023-06-30 Online:2025-10-28 Published:2025-10-25

摘要/Abstract

摘要： 设F_q为一个q元域,q=2^m,且m>1.设正整数h与m互素,对于平移o-多项式$f(x)=x^{2^{h}}$,记$C_{H(f)}^{(2)}$为hyperoval码C_H(f)的二元子域码.利用$C_{H(f)}^{(2)}$的迹函数表示和有限域上的指数和理论,给出了$C_{H(f)}^{(2)}$的重量分布,确定了$C_{H(f)}^{(2)}$及其对偶码$C_{H(f)}^{(2)\perp}$的参数.

关键词: 线性码, hyperoval码, 子域码, 重量分布

Abstract: Let F_q be a finite field of cardinality q, q=2^mand m>1.Assuming that h is a positive integer and coprime with m, for the translation o-polynomial $f(x)=x^{2^{h}}$, let $C_{H(f)}^{(2)}$ be the binary subfield codes of the hyperoval code C_H(f). Based on the trace function representation of $C_{H(f)}^{(2)}$ and the theory of exponential sums over finite fields, the weight distribution of $C_{H(f)}^{(2)}$ is obtained. The parameters of $C_{H(f)}^{(2)}$ and its dual code $C_{H(f)}^{(2)\perp}$ are determined.

Key words: linear code, hyperoval code, subfield code, weight distribution

中图分类号:

程卫东, 程文浩. 关于一类hyperoval码的子域码的重量分布[J]. 兰州理工大学学报, 2025, 51(5): 167-172.

CHENG Wei-dong, CHENG Wen-hao. On weight distribution of a class of subfield codes of hyperoval codes[J]. Journal of Lanzhou University of Technology, 2025, 51(5): 167-172.

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关于一类hyperoval码的子域码的重量分布

On weight distribution of a class of subfield codes of hyperoval codes

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