The subfield codes of hyperoval and conic codes

被引：26

作者：

Heng, Ziling ^{[1
]}

Ding, Cunsheng ^{[2
]}

机构：

[1] Changan Univ, Sch Sci, Xian 710064, Shaanxi, Peoples R China

[2] Hong Kong Univ Sci & Technol, Dept Comp Sci & Engn, Kowloon, Clear Water Bay, Hong Kong, Peoples R China

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2019年 / 56卷

关键词：

Oval; Hyperoval; Conic; Linear code; Subfield code; LINEAR CODES;

D O I：

10.1016/j.ffa.2018.12.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Hyperovals in PG(2, GF(q)) with even q are maximal arcs and an interesting research topic in finite geometries and combinatorics. Hyperovals in PG(2, GF(q)) are equivalent to [q + 2, 3, q] MDS codes over GF(q), called hyperoval codes, in the sense that one can be constructed from the other. Ovals in PG(2, GF(q)) for odd q are equivalent to [q + 1, 3, q - 1] MDS codes over GF(q), which are called oval codes. In this paper, we investigate the binary subfield codes of two families of hyperoval codes and the p-ary subfield codes of the conic codes. The weight distributions of these subfield codes and the parameters of their duals are determined. As a byproduct, we generalize one family of the binary subfield codes to the p-ary case and obtain its weight distribution. The codes presented in this paper are optimal or almost optimal in many cases. In addition, the parameters of these binary codes and p-ary codes seem new. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：308 / 331

页数：24

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