Characterization and enumeration of good punctured polynomials over finite fields (Q1751477)

Summary: A family of good punctured polynomials is introduced. The complete characterization and enumeration of such polynomials are given over the binary field \(\mathbb{F}_2\). Over a nonbinary finite field \(\mathbb{F}_q\), the set of good punctured polynomials of degree less than or equal to \(2\) are completely determined. For \(n \geq 3\), constructive lower bounds of the number of good punctured polynomials of degree \(n\) over \(\mathbb{F}_q\) are given.