Research Interests
Research Interests
My research lies at the intersection of algebraic geometry, coding theory, finite fields, and combinatorics. I am particularly interested in the interaction between geometric structures over finite fields and problems in coding theory. My current research focuses on linear codes associated with (affine) Grassmann and Schubert varieties, algebraic curves over finite fields, and sphere packing problems in Grassmannians.
Linear Codes Associated with (Affine) Grassmann and Schubert Varieties
Linear Codes Associated with (Affine) Grassmann and Schubert Varieties
Grassmannians and their Schubert subvarieties provide natural geometric constructions of linear codes via the Plücker embedding. Suitable open charts of the Grassmannian lead naturally to affine Grassmann codes, providing an affine counterpart to the projective setting. I am interested in the parameters and weight properties of these codes, their generalizations, and their connections with algebraic geometry and finite geometry.
Grassmannians and their Schubert subvarieties provide natural geometric constructions of linear codes via the Plücker embedding. Suitable open charts of the Grassmannian lead naturally to affine Grassmann codes, providing an affine counterpart to the projective setting. I am interested in the parameters and weight properties of these codes, their generalizations, and their connections with algebraic geometry and finite geometry.
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Algebraic Curves over Finite Fields
Algebraic Curves over Finite Fields
Algebraic curves over finite fields provide a rich setting connecting algebraic geometry, function field theory, and coding theory. My interests include the study of curves over finite fields, their rational points and associated function fields, and their applications to algebraic geometry codes.
Algebraic curves over finite fields provide a rich setting connecting algebraic geometry, function field theory, and coding theory. My interests include the study of curves over finite fields, their rational points and associated function fields, and their applications to algebraic geometry codes.
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Sphere Packing Problems in Grassmannians
Sphere Packing Problems in Grassmannians
Grassmannians provide natural metric spaces for studying configurations of subspaces with prescribed separation. I am interested in sphere-packing problems in Grassmannians and their connections to spherical codes and subspace codes.
Grassmannians provide natural metric spaces for studying configurations of subspaces with prescribed separation. I am interested in sphere-packing problems in Grassmannians and their connections to spherical codes and subspace codes.
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