Division criterion for polynomials

Abstract EN

In this short paper we give a generalization of the two criterion in [4], namely: The first is a necessary and sufficient condition for a polynomial f(x) of coefficients in a field F to be divisible by xn - 1.

The second is a necessary and sufficient condition for a polynomial f(x) of coefficients in a field F to be divisible by the cyclotomic polynomial Fp(x) for a prime number p.

In addition to these two criterion, we introduce some consequences.

An important application of these two criteria is to generate good detecting criteria for error-correcting codes.