@article{Alshuhail2025, 
author = {Altaf Alshuhail and Rowena Alma Betty and Lucky Galvez},
title = {Duality of codes over non-unital rings of order six},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {18784-18800},
keywords = {non-unital rings, self-orthogonal codes, self-dual codes, quasi self-dual codes, linear complementary dual, cyclic codes},
url = {https://www.sciopen.com/article/10.3934/math.2025839},
doi = {10.3934/math.2025839},
abstract = {Some basic theory on the duality of codes over two non-unital rings of order    6, namely        H          23       and        H          32       is presented. For a code                      C             over these rings, there is an associated binary code                                C                      a   and a ternary code                                C                      b  . Self-orthogonal, self-dual, and quasi self-dual (QSD) codes over these rings are characterized using the associated codes                                C                      a   and                                C                      b  , and a classification of self-orthogonal codes for short lengths is given. In addition, a building-up construction for self-orthogonal codes is presented, and cyclic and linear complementary dual (LCD) codes over the said rings are introduced.}
}