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.

引用

页码：207 / 226

页数：20

共 7 条

[1] 2-Designs and Codes from Simple Groups L3(q) and Higman-Sims Sporadic Simple Group HS
Moori, Jamshid
Radohery, Georges F. Randriafanomezantsoa
CODING THEORY AND APPLICATIONS, 4TH INTERNATIONAL CASTLE MEETING, 2015, 3 : 281 - 289
[2] SOME DESIGNS AND CODES FROM L-2(q)
Moori, J.
Randriafanomezantsoa-Radohery, G. F.
TRANSACTIONS ON COMBINATORICS, 2014, 3 (01) : 15 - 28
[3] 2-(v, k, 1) Designs with a point-primitive rank 3 automorphism group of affine type
Biliotti, Mauro
Montinaro, Alessandro
Francot, Eliana
DESIGNS CODES AND CRYPTOGRAPHY, 2015, 76 (02) : 135 - 171
[4] SOME STRONGLY REGULAR GRAPHS AND SELF-ORTHOGONAL CODES FROM THE UNITARY GROUP U4(3)
Crnkovic, Dean
Mikulic, Vedrana
Rodrigues, B. G.
GLASNIK MATEMATICKI, 2010, 45 (02) : 307 - 323
[5] Some optimal codes and strongly regular graphs from the linear group L4(3)
Crnkovic, Dean
Crnkovic, Vedrana Mikulic
Rodrigues, B. G.
UTILITAS MATHEMATICA, 2012, 89 : 237 - 255
[6] 2-(v,k,1) Designs Admitting a Primitive Rank 3 Automorphism Group of Affine Type: The Extraspecial and the Exceptional Classes
Montinaro, Alessandro
JOURNAL OF COMBINATORIAL DESIGNS, 2015, 23 (11) : 481 - 498
[7] 2-(v,k,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(v,k,1)$$\end{document} Designs with a point-primitive rank 3 automorphism group of affine type
Mauro Biliotti
Alessandro Montinaro
Eliana Francot
Designs, Codes and Cryptography, 2015, 76 (2) : 135 - 171

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