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arXiv · 2112.06717

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

Yansheng Wu·Jong Yoon Hyun·Yoonjin Lee
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Abstract

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.

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Yansheng Wu, Jong Yoon Hyun, Yoonjin Lee. 2021-12-13. Characterization of $p$-ary functions in terms of association schemes and its applications. https://arxiv.org/abs/2112.06717

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