Indicator functions, v-numbers and Gorenstein rings in the theory of projective Reed-Muller-type codes

Autor:	González-Sarabia, Manuel, Muñoz-George, Humberto, Ordaz, Jorge A., Sáenz-de-Cabezón, Eduardo, Villarreal, Rafael H.
Rok vydání:	2023
Předmět:	Mathematics - Commutative Algebra Computer Science - Information Theory Mathematics - Algebraic Geometry 13P25 14G50 94B27 11T71
Druh dokumentu:	Working Paper
DOI:	10.1007/s10623-024-01437-3
Popis:	For projective Reed--Muller-type codes we give a global duality criterion in terms of the v-number and the Hilbert function of a vanishing ideal. As an application, we provide a global duality theorem for projective Reed--Muller-type codes over Gorenstein vanishing ideals, generalizing the known case where the vanishing ideal is a complete intersection. We classify self dual Reed-Muller-type codes over Gorenstein ideals using the regularity and a parity check matrix. For projective evaluation codes, we give a duality theorem inspired by that of affine evaluation codes. We show how to compute the regularity index of the $r$-th generalized Hamming weight function in terms of the standard indicator functions of the set of evaluation points. Comment: 33 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.13728 Zobrazit plný text záznamu View this record from Arxiv