Characterization of p-ary functions in terms of association schemes and its applications

Yansheng Wu, Jong Yoon Hyun, Yoonjin Lee

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We obtain an explicit criterion for p-ary functions to produce association schemes in terms of their Walsh spectrum. Employing this characterization, we explicitly find a correlation between p-ary bent functions and association schemes; to be more exact, we prove that a p-ary bent function induces a p-class association scheme if and only if the function is weakly regular. As applications of our main criterion, we construct many infinite families of few-class association schemes arising from p-ary functions. Furthermore, we present four classes of p-ary two-weight linear codes, which are constructed from the association schemes produced in this paper.

Original languageEnglish
Article number105576
JournalJournal of Combinatorial Theory. Series A
StatePublished - Apr 2022


  • Association scheme
  • Few-weight linear code
  • Walsh transform
  • p-ary function


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