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Ahmad Muchlis

Publications and source records attributed to Ahmad Muchlis.

4 recordsLinked to original sources
arXiv2021

On bases and the dimensions of twisted centralizer codes

Alahmadi et al. ["Twisted centralizer codes", \emph{Linear Algebra and its Applications} {\bf 524} (2017) 235-249.] introduced the notion of twisted centralizer codes, $\mathcal{C}_{\mathbb{F}_q}(A,γ),$ defined as \[ \mathcal{C}_{\mathbb{F}_q}(A,γ)=\lbrace X \in \mathbb{F}_q^{n \times n}:~\ AX=γXA\rbrace, \] for $A \in \mathbb{F}_q^{n \times n},$ and $γ\in \mathbb{F}_q.$ Moreover, Alahmadi et al. ["On the dimension of twisted centralizer codes", \emph{Finite Fields and Their Applications} {\bf 48} (2017) 43-59.] also investigated the dimension of such codes and obtained upper and lower bounds for the dimension, and the exact value of the dimension only for cyclic or diagonalizable matrices $A.$ Generalizing and sharpening Alahmadi et al.'s results, in this paper, we determine the exact value of the dimension as well as provide an algorithm to construct an explicit basis of the codes for any given matrix $A.$

cs.IT↗
arXiv2017

$Θ_S-$cyclic codes over $A_k$

We study $Θ_S-$cyclic codes over the family of rings $A_k.$ We characterize $Θ_S-$cyclic codes in terms of their binary images. A family of Hermitian inner-products is defined and we prove that if a code is $Θ_S-$cyclic then its Hermitian dual is also $Θ_S-$cyclic. Finally, we give constructions of $Θ_S-$cyclic codes.

cs.IT↗
arXiv2017

Skew-Cyclic Codes over $B_k$

In this paper we study the structure of $θ$-cyclic codes over the ring $B_k$ including its connection to quasi-$\tildeθ$-cyclic codes over finite field $\mathbb{F}_{p^r}$ and skew polynomial rings over $B_k.$ We also characterize Euclidean self-dual $θ$-cyclic codes over the rings. Finally, we give the generator polynomial for such codes and some examples of optimal Euclidean $θ$-cyclic codes.

math.CO↗