Codes on weighted projective planes

Cakiroglu Y., Nardi J., ŞAHİN M.

DESIGNS CODES AND CRYPTOGRAPHY, vol.93, no.10, pp.4141-4171, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 93 Issue: 10
  • Publication Date: 2025
  • Doi Number: 10.1007/s10623-025-01669-x
  • Journal Name: DESIGNS CODES AND CRYPTOGRAPHY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Page Numbers: pp.4141-4171
  • Hacettepe University Affiliated: Yes

Abstract

We comprehensively study weighted projective Reed-Muller (WPRM) codes on weighted projective planes P(1,a,b)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {P}}}(1,a,b)$$\end{document}. We provide the universal Gr & ouml;bner basis for the vanishing ideal of the set Y of Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_q$$\end{document}-rational points of P(1,a,b)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {P}}}(1,a,b)$$\end{document} to get the dimension of the code. We determine the regularity set of Y using a novel combinatorial approach. We employ footprint techniques to compute the minimum distance.