Maximal arcs and extended cyclic codes

被引：6
作者：
De Winter, Stefaan [1 ]
Ding, Cunsheng [2 ]
Tonchev, Vladimir D. [3 ]
机构：
[1] Michigan Technol Univ, Houghton, MI 49921 USA
[2] Hong Kong Univ Sci & Technol, Hong Kong, Peoples R China
[3] Michigan Technol Univ, Houghton, MI 49931 USA
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2019年 / 87卷 / 04期
关键词：
Maximal arc; 2-Design; Two-weight code; Cyclic code; PROJECTIVE-PLANES; WEIGHTS;
D O I：
10.1007/s10623-018-0514-1
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
It is proved that for every d2 such that d-1 divides q-1, where q is a power of 2, there exists a Denniston maximal arc A of degree d in PG(2,q), being invariant under a cyclic linear group that fixes one point of A and acts regularly on the set of the remaining points of A. Two alternative proofs are given, one geometric proof based on Abatangelo-Larato's characterization of Denniston arcs, and a second coding-theoretical proof based on cyclotomy and the link between maximal arcs and two-weight codes.
引用
收藏
页码：807 / 816
页数：10
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