Self-dual codes from quotient matrices of symmetric divisible designs with the dual property

• Published in: Discrete mathematics Vol. 339; no. 2; pp. 409 - 414
• Main Authors: Crnković, Dean, Mostarac, Nina, Rukavina, Sanja
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 06-02-2016
• Subjects: Divisible design; Quotient matrix; Self-dual code; Divisible design; Self-dual code; Quotient matrix
• ISSN: 0012-365X; 1872-681X
• DOI: 10.1016/j.disc.2015.09.004

In this paper we look at codes spanned by the rows of a quotient matrix of a symmetric (group) divisible design (SGDD) with the dual property. We define an extended quotient matrix and show that under certain conditions the rows of the extended quotient matrix span a self-dual code with respect to a certain scalar product. We also show that sometimes a chain of codes can be used to associate a self-dual code to a quotient matrix of a SGDD with the dual property.