Cyclotomic association schemes of broad classes and applications to the construction of combinatorial structures

Abstract

In 2010, G. Fernández, R. Kwashira and L. Martínez gave a new cyclotomy on any product R = n i=1 F qi , where F qi is a finite field with q i elements. They defined a certain subgroup H of the group of units of this product ring R for which the quotient is cyclic. The orbits of the corresponding multiplicative action of the subgroup on the additive group of R are of two types:(1) The cyclotomic cosets of the quotient of the group of units of R over the subgroup H.(2) The n-tuples with arbitrary non-zero elements in positions indicated by a proper subset S of {1, . . . , n} and zeroes elsewhere.