Algebraic invariants of codes on weighted projective planes
Yağmur Çakıroğlu, Mesut Şahi̇n · Journal of Algebra and Its Applications · 2024
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 role in reliably transmitting information on digital communication channels. In this case study, we explore the power of commutative and homological algebraic techniques to study weighted projective Reed–Muller (WPRM) codes on weighted projective spaces of the form [Formula: see text]. We compute minimal free resolutions and thereby obtain Hilbert series for the vanishing ideal of the [Formula: see text]-rational points, and compute main parameters for these codes.