Glasnik Matematicki, Vol. 58, No. 2 (2023), 167-179. \( \)

BLOCK DESIGNS FROM SELF-DUAL CODES OBTAINED FROM PALEY DESIGNS AND PALEY GRAPHS

Dean Crnković, Ana Grbac and Andrea Švob

Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia
e-mail:deanc@math.uniri.hr

Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia
e-mail:abaric@math.uniri.hr

Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia
e-mail:asvob@math.uniri.hr

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.

2020 Mathematics Subject Classification.   05B05, 05E30, 94B05.

Key words and phrases.   Paley design, Paley graph, self-dual code, block design.

Full text (PDF) (access from subscribing institutions only)

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

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