Paper
Hulls of Free Linear Codes over a Non-Unital Ring
Authors
Anup Kushwaha, Om Prakash
Abstract
This paper investigates the hull codes of free linear codes over a non-unital ring . Initially, we examine the residue and torsion codes of various hulls of -linear codes and obtain an explicit form of the generator matrix of the hull of a free -linear code. Then, we propose four build-up construction methods to construct codes with a larger length and hull-rank from codes with a smaller length and hull-rank. Some illustrative examples are also given to support our build-up construction methods. Subsequently, we study the permutation equivalence of two free -linear codes and discuss the hull-variation problem. As an application, we classify optimal free -linear codes for lengths up to .