Partitions into Perfect Codes in the Hamming and Lee Metrics

被引：0
|
作者：
Solov'eva, F., I
机构：
[1] Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 4 Acad. Koptyug Avenue, Novosibirsk
来源：
PROBLEMS OF INFORMATION TRANSMISSION | 2022年 / 58卷 / 03期
基金：
俄罗斯科学基金会;
关键词：
perfect code; perfect code in the Hamming metric; perfect code in the Lee metric; diameter perfect code in the Lee metric; partitions; partitions into perfect codes;
D O I：
10.1134/S003294602203005X
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We propose new combinatorial constructions of partitions into perfect codes in both the Hamming and Lee metrics. Also, we present a new combinatorial construction method for diameter perfect codes in the Lee metric, which is further developed to a construction of partitions into such codes. For the Lee metric, we improve previously known lower bounds on the number of perfect and diameter perfect codes proposed by Etzion in 2011.
引用
收藏
页码：254 / 264
页数：11
相关论文
共 50 条
  • [1] Partitions into Perfect Codes in the Hamming and Lee Metrics
    F. I. Solov’eva
    [J]. Problems of Information Transmission, 2022, 58 : 254 - 264
  • [2] On list decoding of alternant codes in the Hamming and Lee metrics
    Tal, I
    Roth, RM
    [J]. 2003 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY - PROCEEDINGS, 2003, : 364 - 364
  • [3] On perfect Lee codes
    Horak, P.
    [J]. DISCRETE MATHEMATICS, 2009, 309 (18) : 5551 - 5561
  • [4] Diameter Perfect Lee Codes
    Horak, Peter
    AlBdaiwi, Bader F.
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2012, 58 (08) : 5490 - 5499
  • [5] Weighted codes in Lee metrics
    Paul Dorbec
    Sylvain Gravier
    Iiro Honkala
    Michel Mollard
    [J]. Designs, Codes and Cryptography, 2009, 52 : 209 - 218
  • [6] Weighted codes in Lee metrics
    Dorbec, Paul
    Gravier, Sylvain
    Honkala, Iiro
    Mollard, Michel
    [J]. DESIGNS CODES AND CRYPTOGRAPHY, 2009, 52 (02) : 209 - 218
  • [7] ON TRANSITIVE UNIFORM PARTITIONS OF Fn INTO BINARY HAMMING CODES
    Solov'eva, F. I.
    [J]. SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2019, 16 : 886 - 892
  • [8] PARTITIONS OF Fn INTO NON-PARALLEL HAMMING CODES
    Heden, Olof
    Solov'eva, Faina I.
    [J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2009, 3 (04) : 385 - 397
  • [9] GROUP PARTITIONS AND MIXED PERFECT CODES
    LINDSTROM, B
    [J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1975, 18 (01): : 57 - 60
  • [10] Product Constructions for Perfect Lee Codes
    Etzion, Tuvi
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (11) : 7473 - 7481
12345