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Glasnik matematički, Vol. 58 No. 2, 2023.

Original scientific paper

https://doi.org/10.3336/gm.58.2.02

Block designs from self-dual codes obtained from Paley designs and Paley graphs

Dean Crnković orcid id orcid.org/0000-0002-3299-7859 ; Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia
Ana Grbac ; Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia
Andrea Švob ; Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia

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Abstract

In 2002, P. Gaborit introduced two constructions of self-dual codes using quadratic residues, so-called pure and bordered construction, as a generalization of the Pless symmetry codes.
In this paper, we further study conditions under which the pure and the bordered construction using Paley designs and Paley graphs yield self-dual codes.
Special attention is given to the binary and ternary codes.
Further, we construct \(t\)-designs from supports of the codewords of a particular weight in the binary and ternary codes obtained.

Keywords

Paley design, Paley graph, self-dual code, block design.

Hrčak ID:

312009

URI

https://hrcak.srce.hr/312009

Publication date:

21.12.2023.

Visits: 125 *

Publication date: 27 December 2023

Volume: Vol 58

Issue: Svezak 2

Pages: 167-179

DOI: 10.3336/gm.58.2.02

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Paley design, Paley graph, self-dual code, block design.

Block designs from self-dual codes obtained from Paley designs and Paley graphs

Dean Crnkovi c[1]

Email: deanc@math.uniri.hr

Ana Grbac[2]

Email: abaric@math.uniri.hr

Andrea v Svob[3]

Email: asvob@math.uniri.hr

 

[1] Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia

[2] Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia

[3] Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia

Abstract

In 2002, P. Gaborit introduced two constructions of self-dual codes using quadratic residues, so-called pure and bordered construction, as a generalization of the Pless symmetry codes. In this paper, we further study conditions under which the pure and the bordered construction using Paley designs and Paley graphs yield self-dual codes. Special attention is given to the binary and ternary codes. Further, we construct \(t\)-designs from supports of the codewords of a particular weight in the binary and ternary codes obtained.

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