Codes on Subgroups of Weighted Projective Tori

TL;DR

This paper investigates algebraic invariants of codes on subgroups of weighted projective tori and computes key parameters of generalized toric codes within specific weighted projective planes.

Contribution

It introduces methods to determine algebraic invariants and explicitly calculates parameters of toric codes in weighted projective spaces.

Findings

Computed main parameters of generalized toric codes in (1,1,a) weighted projective planes

Identified algebraic invariants relevant to codes on weighted projective tori

Provided a framework for studying codes on subgroups of weighted projective tori

Abstract

We obtain certain algebraic invariants relevant to study codes on subgroups of weighted projective tori inside an $n$-dimensional weighted projective space. As application, we compute all the main parameters of generalized toric codes on these subgroups of tori lying inside a weighted projective plane of the form $\Pp(1,1,a)$.