6 papers
Explicit LCP of MDS Codes and LCD Codes on Hyperelliptic Curves via Mumford Representation
Adler Marques, Yuri da Silva, Saeed Tafazolian
We study algebraic geometry codes on hyperelliptic curves of genus with complementarity properties. Our first contribution is a characterization of non-special divisors…
Jacobian algebras and variation of hyperplane sections
Giovanna Ilardi, Abbas Nasrollah Nejad, Saeed Tafazolian
We study the variation in moduli of hyperplane sections of a hypersurface with at most isolated singularities. Using the Milnor algebra , we give…
On the Maximality, Weierstrass Semigroups, and Automorphism Group of the Curve
João Paulo Guardieiro, Yuri da Silva, Saeed Tafazolian
We study the algebraic curve over defined by , where is a positive integer coprime to the characteristic. We first prove (when is o…
Construction of Non-special Divisors on Kummer Covers With Arbritary Ramification For LCP Codes
Adler Marques, Yuri da Silva, Saeed Tafazolian
Linear Complementary Pairs (LCP) of algebraic geometry (AG) codes offer strong resistance against side-channel and fault-injection attacks, but their construction depends criticall…
Veronese Avoiding Hypersurfaces
Giovanna Ilardi, Abbas Nasrollah Nejad, Saeed Tafazolian
We introduce Veronese-Avoiding hypersurfaces, inspired by the theory of associated forms of Alper--Isaev. In the smooth case, we reinterpret their criterion via Macaulay inverse sy…
Maximal Subcovers of the Skabelund Curve: Uniqueness via Genus and Automorphism Groups
Gilberto B. Almeida Filho, Saeed Tafazolian, Stéfani C. Vieira
We establish a rigidity phenomenon for a family of intermediate covers of the Skabelund curve over . The Skabelund curve, introduced by D.~Skabelund as a cyclic c…