In this paper, we present a basic theory of the duality of linear codes over three of the non-
unital rings of order four; namely,, and as denoted in (Fine, 1993). A new notion of duality is …

In this paper, we describe a new type of DNA codes over two noncommutative rings E and F
of order four with characteristic 2. Our DNA codes are based on quasi self-dual codes over E …

Kim and Ohk (2022) showed that binary self-orthogonal [n, k] codes for various dimensions k
can be useful for the construction of DNA codes based on quasi self-dual codes over a …

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 …

We study the structure of self-orthogonal and self-dual codes over two non-unital rings of
order four, namely, the commutative ring I= a, b| 2 a= 2 b= 0, a 2= b, ab= 0 and the …

Let I be the commutative non-unital ring of order 4 defined by generators and relations. I= a,
b∣ 2 a= 2 b= 0, a 2= b, ab= 0. Alahmadi et al. have classified QSD codes, Type IV 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, ab= 0⟩. We study a recursive construction of …

We study cyclic codes over the ring H of order 4 and characteristic 2 defined by generators
and relations as H=〈 a, b∣ 2 a= 2 b= 0, a 2= 0, b 2= b, ab= ba= 0〉. This is the first time that …

There is a non-unital ring I of order 4 defined by generators and relations as I=〈 a, b| 2 a= 2
b= 0, a 2= b, ab= 0〉. In this paper, we present special constructions of linear codes over I …