8 papers
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…
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…
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…
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…
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…