2021/12/13 by Wu, Yansheng, Hyun, Jong Yoon, Lee, Yoonjin
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2112.06717
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.