Algebraic Invariants of Codes on Weighted Projective Planes
Information Theory
2023-11-07 v2 Commutative Algebra
Algebraic Geometry
math.IT
Abstract
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 . We compute minimal free resolutions and thereby obtain Hilbert series for the vanishing ideal of the -rational points, and compute main parameters for these codes.
Keywords
Cite
@article{arxiv.2301.05313,
title = {Algebraic Invariants of Codes on Weighted Projective Planes},
author = {Yağmur Çakıroğlu and Mesut Şahin},
journal= {arXiv preprint arXiv:2301.05313},
year = {2023}
}