ON THE MINIMAL COSET COVERING FOR A SPECIAL SUBSET IN DIRECT PRODUCT OF TWO FINITE FIELDS

Abstract

In this paper we estimate the minimal number of systems of linear equations of $n+m$ variables over a finite field $F_q$ such that the union of all solutions of all the systems coincides exactly with all elements of $\overset{\ast}{\mathbb{F}_{q}^{n}} \times \overset{\ast}{\mathbb{F}_{q}^{m}}$.