Publication date: 27 December 2023
Volume: Vol 58
Issue: Svezak 2
Pages: 167-179
DOI: 10.3336/gm.58.2.02
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.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
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.
Paley design, Paley graph, self-dual code, block design.
312009
21.12.2023.
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