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Permutation decoding of codes from generalized Paley graphs

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

The generalized Paley graphs \(\text{ GP }(q,k)\) are a generalization of the well-known Paley graphs. Codes derived from the row span of adjacency and incidence matrices from Paley graphs have been studied in Ghinellie and Key (Adv Math Commun 5(1):93–108, 2011) and Key and Limbupasiriporn (Congr Numer 170:143–155, 2004). We examine the binary codes associated with the incidence designs of the generalized Paley graphs obtaining the code parameters \([\frac{qs}{2}, q-1, s]\) or \([qs, q-1,2s]\) where \(s=\frac{q-1}{k}\). By finding explicit PD-sets we show that these codes can be used for permutation decoding.

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Acknowledgments

The authors would like to thank the anonymous referees for their careful review and valuable comments and suggestions. The second author acknowledges partial support from the Faculty of Science, Silpakorn University.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE

    Padmapani Seneviratne

  2. Department of Mathematics, Faculty of Science, Silpakorn University, Nakorn Patom, 73000, Thailand

    Jirapha Limbupasiriporn

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  1. Padmapani Seneviratne
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  2. Jirapha Limbupasiriporn
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Correspondence to Padmapani Seneviratne.

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Seneviratne, P., Limbupasiriporn, J. Permutation decoding of codes from generalized Paley graphs. AAECC 24, 225–236 (2013). https://doi.org/10.1007/s00200-013-0198-8

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  • DOI: https://doi.org/10.1007/s00200-013-0198-8

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