An Elementary Approach to Ax-Katz, McEliece's Divisibility and Applications to Quasi-Perfect Binary 2-Error Correcting Codes

In this paper we present an algorithmic approach to the problem of the divisibility of the number of solutions to a system of polynomial equations. Using this method we prove that all binary cyclic codes with two zeros over F
_2f
and minimum distance 5 are quasi-perfect for f les 10. We also present elementary proofs of divisibility results that, in some cases, improve previous results