Self-dual and self-orthogonal negacyclic codes of length [formula omitted] over a finite field

Abstract

Negacyclic codes form an important class of an algebraically rich family of constacyclic codes due to the following reasons: (i) many examples of good codes can be found among negacyclic codes, (ii) they can be easily encoded using shift registers, and (iii) they can be easily decoded due to their inherent algebraic structure. Two extensively studied subclasses of negacyclic codes are that of self-dual and self-orthogonal codes, which have beautiful underlying algebraic structures, have nice connections with the theory of lattices and Jacobi forms, and are more practical to implement. In this paper, we determine all self-dual and self-orthogonal negacyclic codes of length 2mpn over the finite field Fq with q elements, where p is an odd prime, q is an odd prime power coprime to p and m,n are positive integers.