Relationships between CCZ and EA equivalence classes and corresponding code invariants

Abstract

The purpose of this paper is to provide a brief survey of CCZ and EA equivalence for functions f : G → N where G and N are finite and N is abelian, and, for the case f : ℤmp → ℤmp, to investigate two codes derived from f, inspired by these equivalences. In particular we show the dimension of the kernel of each code determines a new invariant of the corresponding equivalence class. We present computational results for p = 2 and small m.