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.
Bibliographical noteFunding Information:
Y. Wu was supported by the National Natural Science Foundation of China (Grant No. 12101326 ) and the Natural Science Foundation of Jiangsu Province (Grant No. BK20210575 ). J.Y. Hyun was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MEST ) ( NRF-2017R1D1A1B05030707 ). Y. Lee was supported by the Ewha Womans University Research Grant of 2021, Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177 ) and the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MEST ) ( NRF-2017R1A2B2004574 ).
© 2021 Elsevier Inc.
- Association scheme
- Few-weight linear code
- Walsh transform
- p-ary function