Abstract:
This talk is dedicated to the study of weighted projective Reed-Muller (WPRM) codes on weighted projective planes P(1,a,b). These codes are formed by the evaluations of weighted-degree-d polynomials at the set Y of Fq-rational points of P(1,a,b). To handle the dimension and the minimum distance of these codes, we rely on combinatorial techniques, coming from the toric geometry. We also determine the regularity set of Y using this novel combinatorial approach. We notably employ footprint techniques to compute the minimum distance, highlighting some limits of this method. This talk is based on a joint work with Yağmur Çakıroğlu and Mesut Şahin (arXiv:2410.11968).