Thirty-Second International Conference on Learning

Abstract

Almost difference sets play significant roles in the fields of group theory, combinatorics, and coding theory, offering diverse applications. The classical method of combining specific cyclotomic classes within a finite field has been used in generating almost difference sets. In this study, we present new construction of almost difference sets using cyclotomic classes of order 18 (with and without the residue zero) of the finite field GF(q), where q is a prime of the form q=18n+1 for positive integers n≥1 and q<1000. Our construction employs an exhaustive Python-based computer search, systematically computing the single cyclotomic class and the unions of two classes up to seventeen classes. Additionally, we ascertain the equivalence of the generated almost difference sets with identical parameters, up to complementation. The research findings will contribute to the literature a new construction of almost difference sets via cyclotomy of order 18.