Algebraic invariants of codes on weighted projective planes

Cakiroglu Y., ŞAHİN M.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2024
  • Doi Number: 10.1142/s0219498825503487
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Hacettepe University Affiliated: Yes

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 P(1, 1,b). We compute minimal free resolutions and thereby obtain Hilbert series for the vanishing ideal of the F-q-rational points, and compute main parameters for these codes.