@article{Alahmadi2024, 
author = {Adel Alahmadi and Tamador Alihia and Patrick Solé},
title = {The build up construction for codes over a non-commutative non-unitary ring of order    9},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {18278-18307},
keywords = {non-unitary rings, self-dual codes, build-up construction},
url = {https://www.sciopen.com/article/10.3934/math.2024892},
doi = {10.3934/math.2024892},
abstract = {The build-up method is a powerful class of propagation rules that generate self-dual codes over finite fields and unitary rings. Recently, it was extended to non-unitary rings of order four to generate quasi self-dual codes. In the present paper we introduce three such propagation rules to generate self-orthogonal, one-sided self-dual, and self-dual codes over a special non-unitary ring of order 9. As an application, we classify the three categories of codes in lengths at most    7  , up to monomial equivalence. Mass formulas for the three classes of codes considered ensure that the classification is complete.}
}