Quasi-symmetric designs and codes meeting the Grey-Rankin bound
type: Item
instance of: scholarly article
title: Quasi-symmetric designs and codes meeting the Grey-Rankin bound
zbMATH Open document ID: 0873.05011
author: Gary McGuire
published in: Journal of Combinatorial Theory. Series A
publication date: 1997-10-26T00:00:00Z
review text: A characterization of the parameters of binary codes meeting the Grey-Rankin bound is proved. As pointed out earlier by \textit{D. Jungnickel} and the reviewer [Des. Codes Cryptography 1, No. 3, 247-253 (1991; Zbl 0766.05009)], quasi-symmetric designs with the property that the symmetric difference of any two blocks is either a block or a complement of a block give rise to linear codes meeting the Grey-Rankin bound. The present characterization implies that all linear binary codes meeting the Grey-Rankin bound are of this type.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 94B65
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 1016844
zbMATH Keywords: binary codes
zbMATH Keywords: Grey-Rankin bound
zbMATH Keywords: quasi-symmetric designs
reviewed by: Vladimir D. Tonchev
MaRDI profile type: Publication
full work available at URL: jcta.1997.2765
OpenAlex ID: W1967009268
cites work: Transitive groups of collineations on certain designs
cites work: Geometric invariants for quasi-symmetric designs
cites work: Binary codes and quasi-symmetric designs
cites work: Q5672648
cites work: Q4000288
cites work: Four fundamental parameters of a code and their combinatorial significance
cites work: Q5707657
cites work: Q4119093
cites work: On the \([28,7,12]\) binary self-complementary codes and their residuals
cites work: Correction to 'Some Bounds for Error-Correcting Codes'
cites work: Strongly Regular Graphs Derived from Combinatorial Designs
cites work: Symplectic groups, symmetric designs, and line ovals
cites work: Exponential numbers of two-weight codes, difference sets and symmetric designs
cites work: Exponential number of quasi-symmetric SDP designs and codes meeting the Grey-Rankin bound
cites work: On quasi-symmetric 2-(28, 12, 11) and 2-(36, 16, 12) designs
cites work: Q4146667
cites work: Q3960709
cites work: On the minimal points of positive definite quadratic forms
cites work: Quasi-symmetric designs, codes, quadrics, and hyperplane sections
cites work: Q4004139
DOI: 10.1006/JCTA.1997.2765
description: scientific article; zbMATH DE number 1016844