19 citations · 55 across the 12 of their papers we have counts for
18 papers
Hull Variation in Symplectic Linear Codes
Kanat Abdukhalikov, Somi Gupta, Duy Ho
We study the variation of hull dimensions of symplectic linear codes under equivalence transformations preserving the symplectic distance. For a symplectic linear code , we intr…
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…
Ovoids in the cyclic presentation of PG(3,q)
Kanat Abdukhalikov, Simeon Ball, Duy Ho +1
We consider the cyclic presentation of whose points are in the finite field and describe the known ovoids therein. We revisit the set , co…
Extended cyclic codes, maximal arcs and ovoids
Kanat Abdukhalikov, Duy Ho
We show that extended cyclic codes over with parameters , , determine regular hyperovals. We also show that extended cyclic codes with parameters $…
Polar coordinates view on KM-arcs
Kanat Abdukhalikov, Duy Ho
We study presentations of KM-arcs in polar coordinates. New characterizations on the points set of KM-arcs are obtained in terms of power sums and bilinear forms. We also construct…
Vandermonde sets and hyperovals
Kanat Abdukhalikov, Duy Ho
We consider relationships between Vandermonde sets and hyperovals. Hyperovals are Vandermonde sets, but, in general, Vandermonde sets are not hyperovals. We give necessary and suff…
Equivalence classes of Niho bent functions
K. Abdukhalikov
Equivalence classes of Niho bent functions are described for all known types of hyperovals.
Bent functions and line ovals
Kanat Abdukhalikov
In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functi…
Symplectic spreads, planar functions and mutually unbiased bases
Kanat Abdukhalikov
In this paper we give explicit descriptions of complete sets of mutually unbiased bases (MUBs) and orthogonal decompositions of special Lie algebras obtained fro…
Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets
Kanat Abdukhalikov, Eiichi Bannai, Sho Suda
H. Cohn et. al. proposed an association scheme of 64 points in R^{14} which is conjectured to be a universally optimal code. We show that this scheme has a generalization in terms…
Unimodular lattices in dimensions 14 and 15 over the Eisenstein integers
Kanat Abdukhalikov, Rudolf Scharlau
All indecomposable unimodular hermitian lattices in dimensions 14 and 15 over the ring of integers in are determined. Precisely one lattice in dimension 14…