Classification of extremal type II Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_4$$\end{document}-codes of length 24

被引：0
作者：
Akihiro Munemasa
Rowena Alma L. Betty
机构：
[1] Tohoku University,Graduate School of Information Sciences
[2] University of the Philippines-Diliman,Institute of Mathematics
来源：
Designs, Codes and Cryptography | 2024年 / 92卷 / 3期
关键词：
Self-dual code; Type II code; Free code; Extremal code; Classification; 94B25; 15A63;
D O I：
10.1007/s10623-023-01293-7
中图分类号：
学科分类号：
摘要：
In this paper, we give a classification of extremal Type II Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_4$$\end{document}-codes of length 24. This is equivalent to a classification of 4-frames of the Leech lattice up to the action of the automorphism group.
引用
收藏
页码：771 / 785
页数：14
相关论文
共 26 条
[1]  
Bachoc C(1997)Type II codes over IEEE Trans. Inform. Theory 43 969-976
[2]  
Bonnecaze A(1999)Type II codes, even unimodular lattices, and invariant rings IEEE Trans. Inform. Theory 45 1194-1205
[3]  
Mourrain B(2019)Classification of self-dual codes of length 20 over Lecture Notes Comput. Sci. 11929 64-77
[4]  
Solé P(2009) and length at most 18 over J. Combin. Inform. Syst. Sci. 34 51-66
[5]  
Bannai E(1997)Mass formula for self-orthogonal codes over J. Symbol. Comput. 24 235-265
[6]  
Dougherty ST(1993)The Magma algebra system I: the user language J. Combin. Theory Series A 62 30-45
[7]  
Harada M(2011)Self-dual codes over the integers modulo 4 Discret. Math. 311 2148-2157
[8]  
Oura M(2013)On the residue codes of extremal Type II Mathematische Zeitschrift 274 685-700
[9]  
Betty RAL(2009)-codes of lengths 32 and 40 Math. Comput. 78 1787-1796
[10]  
Munemasa A(1998)Residue codes of extremal Type II IEEE Trans. Inform. Theory 44 800-809
123