ON SOME CODES FROM RANK 3 PRIMITIVE ACTIONS OF THE SIMPLE CHEVALLEY GROUP G2(q)

被引：1
|
作者：
Le, Tung [1 ]
Rodrigues, Bernardo G. [1 ]
机构：
[1] Univ Pretoria, Dept Math & Appl Math, ZA-0028 Hatfield, South Africa
来源：
ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2023年 / 17卷 / 01期
基金：
新加坡国家研究基金会;
关键词：
Strongly regular graph; modular representation theory; linear code; PERMUTATION-GROUPS; BINARY-CODES; DESIGNS; GRAPHS;
D O I：
10.3934/amc.2022016
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Let G(2)(q) be a Chevalley group of type G(2) over a finite field Fq. Considering the G(2) (q)-primitive action of rank 3 on the set of q(3) (q(3)-1)/2 hyper-2 planes of type O-6(-) (q) in the 7-dimensional orthogonal space PG(7, q), we study the designs, codes, and some related geometric structures. We obtained the main parameters of the codes, the full automorphism groups of these structures, and geometric descriptions of the classes of minimum weight codewords.
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页码：207 / 226
页数：20
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