Type IV codes over a non-local non-unital ring
Author
Alahmadi, Adel
Alkathiry, Amani
Altassan, Alaa
Basaffar, Widyan
Bonnecaze, Alexis
Shoaib, Hatoon
Solé, Patrick
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/431610.22199/issn.0717-6279-2020-04-0060
Abstract
There is a local ring H of order 4, without identity for the multiplication, defined by generators and relations as
H =?a, b | 2a = 2b = 0, a2 = 0, b2 = b, ab = ba = 0?.
We classify self orthogonal codes of length n and size 2n (called here quasi self-dual codes or QSD) up to the length n = 6. In particular, we classify quasi Type IV codes (a subclass of Type IV codes, viz QSD codes with even weights) up to n = 6.