Algebraic invariants of codes on weighted projective planes

Cakiroglu Y., ŞAHİN M.

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

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1142/s0219498825503487
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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.