19 citations · 55 across the 12 of their papers we have counts for
9 papers · 1 filter
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…
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…