AN UPPER BOUND FOR THE COMPLEXITY OF LINEARIZED COVERINGS IN A FINITE FIELD

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Submitted: 2025-02-23; Published: 2025-02-23

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Abstract

The minimal number of systems of linear equations with n unknowns over a finite field Fq, such that the union of all solutions of the systems forms an exact cover for a given subset in Fqn, is the complexity of a linearized covering. An upper bound for the complexity for “almost all” subsets in Fqn is presented.