Characterization and Enumeration of Good Punctured Polynomials over Finite Fields

الملخص EN

A family of good punctured polynomials is introduced.

The complete characterization and enumeration of such polynomials are given over the binary field F2.

Over a nonbinary finite field Fq, the set of good punctured polynomials of degree less than or equal to 2 are completely determined.

For n≥3, constructive lower bounds of the number of good punctured polynomials of degree n over Fq are given.