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- Title
Type IV codes over a non-unital ring.
- Authors
Alahmadi, Adel; Altassan, Alaa; Basaffar, Widyan; Shoaib, Hatoon; Bonnecaze, Alexis; Solé, Patrick
- Abstract
There is a special local ring E of order 4 , without identity for the multiplication, defined by E = 〈 a , b | 2 a = 2 b = 0 , a 2 = a , b 2 = b , a b = a , b a = b 〉. We study the algebraic structure of linear codes over that non-commutative local ring, in particular their residue and torsion codes. We introduce the notion of quasi self-dual codes over E , and Type IV codes, that is quasi self-dual codes whose all codewords have even Hamming weight. We study the weight enumerators of these codes by means of invariant theory, and classify them in short lengths.
- Subjects
NONCOMMUTATIVE rings; LOCAL rings (Algebra); HAMMING weight; TORSION; LINEAR codes
- Publication
Journal of Algebra & Its Applications, 2022, Vol 21, Issue 7, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498822501420