Shakir Ali

collaborators

4 papers

cs.IT2026

On the generalization of $g$ -circulant MDS matrices

Atif Ahmad Khan, Shakir Ali, Bhupendra Singh

A matrix $M$ over the finite field $F_{q}$ is called \emph{maximum distance separable} (MDS) if all of its square submatrices are non-singular. These MDS matrices are very…

cs.IT2026

MDS matrices from skew polynomials with automorphisms and derivations

Atif Ahmad Khan, Shakir Ali, Elif Segah Oztas +1

Maximum Distance Separable (MDS) matrices play a central role in coding theory and symmetric-key cryptography due to their optimal diffusion properties. In this paper, we present a…

cs.IT2025

On the construction of Cauchy MDS matrices over Galois rings via nilpotent elements and Frobenius maps

Shakir Ali, Atif Ahmad Khan, Abhishek Kesarwani

Let $s, m$ be the positive integers and $p$ be any prime number. Next, let $GR (p^{s}, p^{s m})$ be a Galois ring of characteristic $p^{s}$ and cardinality $p^{s m}$ . In the present paper,…

cs.IT2025

Quasi-recursive MDS Matrices over Galois Rings

Shakir Ali, Atif Ahmad Khan, Abhishek Kesarwani +1

Let $p$ be a prime and $s, m, n$ be positive integers. This paper studies quasi-recursive MDS matrices over Galois rings $GR (p^{s}, p^{s m})$ and proposes various direct construction…

On the generalization of g-circulant MDS matrices

MDS matrices from skew polynomials with automorphisms and derivations

On the construction of Cauchy MDS matrices over Galois rings via nilpotent elements and Frobenius maps

Quasi-recursive MDS Matrices over Galois Rings

On the generalization of $g$ -circulant MDS matrices