Cyclic and Negacyclic Codes of Length \(2^m\) over Finite Fields

Abstract

Let \({F}_q\) be a finite field of odd order \(q\). In this note, the generator polynomials and the numbers of all self-dual and self-orthogonal cyclic and negacyclic codes of length \(2^m\) over \({F}_q\) are precisely characterized.