Constructions of optimal quaternary constant weight codes via group divisible designs

被引：5

作者：

Wu, Dianhua ^{[1
,2
]}

Fan, Pingzhi ^{[2
]}

机构：

[1] Guangxi Normal Univ, Dept Math, Guilin 541004, Peoples R China

[2] SW Jiaotong Univ, Keylab Informat Coding & Transmiss, Chengdu 610031, Peoples R China

来源：

DISCRETE MATHEMATICS | 2009年 / 309卷 / 20期

关键词：

Generalized Steiner system; Constant weight code; k-*GDD; Skew starter; GENERALIZED STEINER SYSTEMS; BLOCK SIZE 3;

D O I：

10.1016/j.disc.2009.05.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Generalized Steiner systems GS(2. k, v. g) were first introduced by Etzion and used to construct optimal constant weight codes over an alphabet of size g + I with minimum Hamming distance 2k - 3, in which each codeword has length v and weight k. As to the existence of a GS(2. k, v. g), a lot of work has been done for k = 3, while not so much is known for k = 4. The notion k-*GDD was first introduced by Chen et al and used to construct GS(2. 3, v. 6) The necessary condition for the existence of a 4-*GDD(6 '') is v >= 14. In this paper, it is proved that there exists a 4-*GDD(6 '') for any prime power v equivalent to 15, 7 (mod 8) and v >= 19. By using this result, the known results on the existence of optimal quaternary constant weight codes are then extended. (C) 2009 Elsevier B.V. All rights reserved

引用

页码：6009 / 6013

页数：5

共 23 条

[11] GE G, 2002, ACTA MATH APPL SIN-E, V18, P561
[12] Construction of optimal ternary constant weight codes via Bhaskar Rao designs
Ge, Gennian
[J]. DISCRETE MATHEMATICS, 2008, 308 (13) : 2704 - 2708
[13] [Ge Gennian 葛根年], 2003, [数学研究与评论, Journal of Mathematical Research and Exposition], V23, P391
[14] Some new optimal quaternary constant weight codes
Ge, GN
Wu, DH
[J]. SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES, 2005, 48 (02): : 192 - 200
[15] 4-*GDDs(3n) and generalized Steiner systems GS(2, 4, ν, 3)
Ge, GN
Wu, D
[J]. JOURNAL OF COMBINATORIAL DESIGNS, 2003, 11 (06) : 381 - 393
[16] SOME TACTICAL CONFIGURATIONS
HANANI, H
[J]. CANADIAN JOURNAL OF MATHEMATICS, 1963, 15 (04): : 702 - &
[17] Existence of generalized Steiner systems GS(2,4,υ,2)
Ji, L
Wu, D
Zhu, L
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2005, 36 (01) : 83 - 99
[18] Mills W. H., 1974, P 5 SE C COMB GRAPH, P573
[19] Phelps K, 1999, ARS COMBINATORIA, V53, P133
[20] Phelps K, 1997, J COMB DES, V5, P417, DOI 10.1002/(SICI)1520-6610(1997)5:6<417::AID-JCD3>3.0.CO

← 1 2 3 →