An enumeration of 1-perfect ternary codes

被引：3
|
作者：
Shi, Minjia [1 ,2 ]
Krotov, Denis S. [3 ]
机构：
[1] Anhui Univ, Sch Math Sci, Key Lab Intelligent Comp & Signal Proc, Minist Educ, Hefei, Anhui, Peoples R China
[2] Xidian Univ, State Key Lab Integrated Serv Networks, Xian 710071, Peoples R China
[3] Sobolev Inst Math, Novosibirsk 630090, Russia
来源：
DISCRETE MATHEMATICS | 2023年 / 346卷 / 07期
基金：
中国国家自然科学基金;
关键词：
Perfect codes; Ternary codes; Concatenation; Switching; FULL-RANK TILINGS; ERROR-CORRECTING CODES; ARY QUASI-GROUPS; PERFECT CODES; CONSTRUCTION;
D O I：
10.1016/j.disc.2023.113437
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study codes with parameters of the ternary Hamming (n = (3m - 1)/2, 3n-m, 3) code, i.e., ternary 1-perfect codes. The rank of the code is defined to be the dimension of its affine span. We characterize ternary 1-perfect codes of rank n -m + 1, count their number, and prove that all such codes can be obtained from each other by a sequence of two -coordinate switchings. We enumerate ternary 1-perfect codes of length 13 obtained by concatenation from codes of lengths 9 and 4; we find that there are 93241327 equivalence classes of such codes. (c) 2023 Elsevier B.V. All rights reserved.
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页数：16
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