arXiv subjects

Joydeb Pal

Publications and source records attributed to Joydeb Pal.

3 recordsLinked to original sources

arXiv2022

On the $\ell$-DLIPs of codes over finite commutative rings

Generalizing the linear complementary duals, the linear complementary pairs and the hull of codes, we introduce the concept of $\ell$-dimension linear intersection pairs ($\ell$-DLIPs) of codes over a finite commutative ring $(R)$, for some positive integer $\ell$. In this paper, we study $\ell$-DLIP of codes over $R$ in a very general setting by a uniform method. Besides, we provide a necessary and sufficient condition for the existence of a non-free (or free) $\ell$-DLIP of codes over a finite commutative Frobenius ring. In addition, we obtain a generator set of the intersection of two constacyclic codes over a finite chain ring, which helps us to get an important characterization of $\ell$-DLIP of constacyclic codes. Finally, the $\ell$-DLIP of constacyclic codes over a finite chain ring are used to construct new entanglement-assisted quantum error correcting (EAQEC) codes.

cs.IT↗

arXiv2018

On decoding procedures of intertwining codes

One of the main weakness of the family of centralizer codes is that its length is always $n^2$. Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form $nk$. We establish two decoding methods which can be fitted to intertwining codes as well as for any linear codes. We also show an inclusion of linear codes into a special class of intertwining codes.

cs.IT↗

arXiv2017

Generalized twisted centralizer codes

An important code of length $n^2$ is obtained by taking centralizer of a square matrix over a finite field $\mathbb{F}_q$. Twisted centralizer codes, twisted by an element $a \in \mathbb{F}_q$, are also similar type of codes but different in nature. The main results were embedded on dimension and minimum distance. In this paper, we have defined a new family of twisted centralizer codes namely generalized twisted centralizer (GTC) codes by $\mathcal{C}(A,D):= \lbrace B \in \mathbb{F}_q^{n \times n}|AB=BAD \rbrace$ twisted by a matrix $D$ and investigated results on dimension and minimum distance. Parity-check matrix and syndromes are also investigated. Length of the centralizer codes is $n^2$ by construction but in this paper, we have constructed centralizer codes of length $(n^2-i)$, where $i$ is a positive integer. In twisted centralizer codes, minimum distance can be at most $n$ when the field is binary whereas GTC codes can be constructed with minimum distance more than $n$.

cs.IT↗