There are exactly two non-commutative rings of size 4, namely, and its opposite ring. These
rings are non-unital. A subset of is defined with the help of simplicial complexes, and utilized …

In this article, we construct linear codes over the commutative non-unital ring I of size four.
We obtain their Lee-weight distributions and study their binary Gray images. Under certain …

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 4 …

Let $ E $ and $ I $ denote the two non-unital rings of order 4 in the notation of (Fine, 93)
defined by generators and relations as $ E=\langle a, b\mid 2a= 2b= 0, a^ 2= a, b^ 2= b, ab …

In the last 60 years coding theory has been studied a lot over finite fields 𝔽 q or commutative
rings ℛ with unity. Although in 1 9 9 3, a study on the classification of the rings (not …

We consider the commutative non-unitary ring of order four defined as I={a, b| 2a= 0, 2b= 0,
a 2= b, ab= 0}. Self-orthogonal codes for a symplectic inner product over I are introduced. A …