12 citations · 16 across the 6 of their papers we have counts for
7 papers
Codes on Weighted Projective Planes
Yağmur Çakıroğlu, Jade Nardi, Mesut Şahin
We comprehensively study weighted projective Reed-Muller (WPRM) codes on weighted projective planes . We provide the universal Gröbner basis for the vanishing id…
Algebraic Invariants of Codes on Weighted Projective Planes
Yağmur Çakıroğlu, Mesut Şahin
Weighted projective spaces are natural generalizations of projective spaces with a rich structure. Projective Reed-Muller codes are error-correcting codes that played an important…
Computing Vanishing Ideals for Toric Codes
Mesut Şahin
Motivated by applications to the theory of error-correcting codes, we give methods for computing a generating set for the ideal generated by -graded polynomials vanishing on cer…
Betti numbers for certain Cohen-Macaulay tangent cones
Mesut Şahin, Nil Şahin
In this article, we compute Betti numbers for a Cohen-Macaulay tangent cone of a monomial curve in the affine -space corresponding to a pseudo symmetric numerical semigroup. As…
Equations defining recursive extensions as set theoretic complete intersections
Tran Hoai Ngoc Nhan, Mesut Şahin
Based on the fact that projective monomial curves in the plane are complete intersections, we give an effective inductive method for creating infinitely many monomial curves in the…
Toric ideals of simple surface singularities
Gülay Kaya, Pınar Mete, Mesut Şahin
In this paper, we study a class of toric ideals obtained by using some geometric data of ADE trees which are the minimal resolution graphs of rational surface singularities. We com…
Multigraded Hilbert function and toric complete intersection codes
Mesut Şahin, Ivan Soprunov
Let be a complete -dimensional simplicial toric variety with homogeneous coordinate ring . We study the multigraded Hilbert function of reduced -dimensional subs…