19 citations · 55 across the 12 of their papers we have counts for
8 papers · 1 filter
New distance bounds for one-generator quasi-cyclic codes with applications to Hermitian LCD codes and entanglement-assisted quantum codes
Kanat Abdukhalikov, Duy Ho, Rasha M. Shat
We introduce lower bounds on the minimum distance of one-generator quasi-cyclic codes of arbitrary index, obtained by puncturing and shortening the code at the level of its blocks.…
Quasi-twisted codes and their connection with additive constacyclic codes over finite fields
Kanat Abdukhalikov, Gyanendra K. Verma
In this paper, we study quasi-twisted codes and their relationship with additive constacyclic codes through a polynomial-based approach. We first present a polynomial characterizat…
On the equivalence between additive and linear codes
Kanat Abdukhalikov, Duy Ho
Additive codes have attracted considerable attention for their potential to outperform linear codes. However, distinguishing strictly additive codes from those that are equivalent…
Two Families of Linear Codes Containing Non-GRS MDS Codes
Kanat Abdukhalikov, Gyanendra K. Verma
We construct two new families of linear codes by modifying the generator matrices of generalized Reed-Solomon (GRS) codes. For these codes, we explicitly derive parity-check matric…
Some constructions of non-generalized Reed-Solomon MDS Codes
Kanat Abdukhalikov, Cunsheng Ding, Gyanendra K. Verma
We investigate two classes of extended codes and provide necessary and sufficient conditions for these codes to be non-GRS MDS codes. We also determine the parity check matrices fo…
Linear Complementary Pairs of Quasi-Cyclic and Quasi-Twisted Codes
Kanat Abdukhalikov, Duy Ho, San Ling +1
In this paper, we provide a polynomial characterization of linear complementary pairs of quasi-cyclic and quasi-twisted codes of index 2. We also give several examples of linear co…
Linear complementary dual quasi-cyclic codes of index 2
Kanat Abdukhalikov, Duy Ho, San Ling +1
We provide a polynomial approach to investigate linear complementary dual (LCD) quasi-cyclic codes over finite fields. We establish necessary and sufficient conditions for LCD quas…
Quasi-cyclic codes of index 2
Kanat Abdukhalikov, Askar S. Dzhumadil'daev, San Ling
We study quasi-cyclic codes of index 2 over finite fields. We give a classification of such codes. Their duals with respect to the Euclidean, symplectic and Hermitian inner product…