Quasi type IV codes over a non-unital ring

• Published in: Applicable algebra in engineering, communication and computing Vol. 32; no. 3; pp. 217 - 228
• Main Authors: Alahmadi, Adel, Altassan, Alaa, Basaffar, Widyan, Bonnecaze, Alexis, Shoaib, Hatoon, Solé, Patrick
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021; Springer Nature B.V; Springer Verlag
• Subjects: Artificial Intelligence; Binary system; Canonical forms; Codes; Computer Hardware; Computer Science; Information Theory; Linear codes; Mathematical analysis; Mathematics; Matrix algebra; Matrix methods; Multiplication; Original Paper; Permutations; Rings (mathematics); Symbolic and Algebraic Manipulation; Theory of Computation; Codes; Additive; Mass formulas; Type IV codes; Secondary 16 A10; Rings; Primary 94 B05; Type IV codes Mathematics Subject Classification Primary 94 B05; Additive 4 -codes

There is a local ring I of order 4,  without identity for the multiplication, defined by generators and relations as I = ⟨ a , b ∣ 2 a = 2 b = 0 , a 2 = b , a b = 0 ⟩ . We give a natural map between linear codes over I and additive codes over F 4 , that allows for efficient computations. We study th...