Papers by shyambhu Mukherjee
ArXiv, 2017
An important code of length $n^2$ is obtained by taking centralizer of a square matrix over a fin... more 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 $n$.
Journal of Discrete Mathematical Sciences and Cryptography
One of the main weakness of the family of centralizer codes is that its length is always n 2. Thu... more 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.
Journal of Discrete Mathematical Sciences and Cryptography, Apr 2, 2020
One of the main weakness of the family of centralizer codes is that its length is always n 2. Thu... more 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.
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Papers by shyambhu Mukherjee