Characterization and Enumeration of Good Punctured Polynomials over Finite Fields

Abstract

A family of good punctured polynomials is introduced. The complete characterization and enumeration of such polynomials are given over the binary fieldF2. Over a nonbinary finite fieldFq, the set of good punctured polynomials of degree less than or equal to2are completely determined. Forn≥3, constructive lower bounds of the number of good punctured polynomials of degreenoverFqare given.