TY - JOUR AU - Alahmadi, Adel AU - Alkathiry, Amani AU - Altassan, Alaa AU - Basaffar, Widyan AU - Bonnecaze, Alexis AU - Shoaib, Hatoon AU - Solé, Patrick PY - 2020/07/28 Y2 - 2024/03/29 TI - Quasi self-dual codes over non-unital rings of order six JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 39 IS - 4 SE - DO - 10.22199/issn.0717-6279-2020-04-0066 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4337 SP - 1083-1095 AB - <p><em>There exist two semi-local rings of order 6 without identity for the multiplication. We classify up to coordinate permutation self-orthogonal codes of length n and size 6<sup>n/2 </sup>over these rings (called here quasi self-dual codes or QSD) till the length n = 8. To any such code is attached canonically a </em>ℤ<em><sub>6</sub></em><em>-code, which, when self-dual, produces an unimodular lattice by Construction A. </em></p> ER -