Indicator functions, \(\mathrm{v}\)-numbers and Gorenstein rings in the theory of projective Reed-Muller-type codes
DOI10.1007/s10623-024-01437-3MaRDI QIDQ6632035
Manuel González Sarabia, Humberto Muñoz-George, Jorge A. Ordaz, Eduardo Sáenz-de-Cabezón, Rafael H. Villarreal
Publication date: 4 November 2024
Published in: Designs, Codes and Cryptography (Search for Journal in Brave)
regularityfinite fieldsdegreeHilbert functionsminimum distanceindicator functionsstandard monomialsReed-Muller-type codes\(\mathrm{h}\)-vectors\(\mathrm{v}\)-number
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)
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