Pseudo Quasi-3 Designs and Their Applications to Coding Theory

被引：3

作者：

Bracken, Carl ^{[1
]}

机构：

[1] Univ Coll Dublin, Sch Math Sci, Claude Shannon Inst, Dublin, Ireland

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2009年 / 17卷 / 05期

关键词：

quasi-symmetric design; quasi-3; design; Grey Rankin bound; error correcting code; SYMMETRICAL DESIGNS; CODES;

D O I：

10.1002/jcd.20208

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define a pseudo quasi-3 design as a symmetric design with the property that the derived and residual designs with respect to at least one block are quasi-symmetric. Quasi-symmetric designs can be used to construct optimal self complementary codes. In this article we give a construction of an infinite family of pseudo quasi-3 designs whose residual designs allow us to construct a family of codes with a new parameter set that meet the Grey Rankin bound. (C) 2009 Wiley Periodicals, Inc. J Combin Designs 17: 411-418, 2009

引用

页码：411 / 418

页数：8

共 12 条

[1] TRANSITIVE GROUPS OF COLLINEATIONS ON CERTAIN DESIGNS [J].

BLOCK, RE .

PACIFIC JOURNAL OF MATHEMATICS, 1965, 15 (01) :13-&

[2] Duals of quasi-3 designs are not necessarily quasi-3 [J].

Bracken, Carl ;

McGuire, Gary .

DESIGNS CODES AND CRYPTOGRAPHY, 2007, 44 (1-3) :157-167

[3] New classes of self-complementary codes and quasi-symmetric designs [J].

Bracken, Carl .

DESIGNS CODES AND CRYPTOGRAPHY, 2006, 41 (03) :319-323

[4] New quasi-symmetric designs constructed using mutually orthogonal Latin squares and Hadamard matrices [J].

Bracken, Carl ;

McGuire, Gary ;

Ward, Harold .

DESIGNS CODES AND CRYPTOGRAPHY, 2006, 41 (02) :195-198

[5]

Cameron P. J., 1991, DESIGNS GRAPHS CODES

[6]

CAMERON PJ, 1973, GEOM DEDICATA, V2, P213

[7]

Jungnickel D., 1991, Designs, Codes and Cryptography, V1, P247, DOI 10.1007/BF00123764

[8] ON SYMMETRICAL AND QUASI-SYMMETRICAL DESIGNS WITH THE SYMMETRICAL DIFFERENCE PROPERTY AND THEIR CODES [J].

JUNGNICKEL, D ;

TONCHEV, VD .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 1992, 59 (01) :40-50

[9] Quasi-symmetric designs and codes meeting the Grey-Rankin bound [J].

McGuire, G .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 1997, 78 (02) :280-291

[10] ON THE DUAL OF SOME BALANCED INCOMPLETE BLOCK DESIGNS [J].

SHRIKHANDE, SS .

BIOMETRICS, 1952, 8 (01) :66-72

← 1 2 →