Bases for Riemann–Roch spaces of linearized function fields with applications to generalized algebraic geometry codes

Several applications of function fields over finite fields, or equivalently, algebraic curves over finite fields, require computing bases for Riemann–Roch spaces. In this paper, we determine explicit bases for Riemann–Roch spaces of linearized function fields, and we give a lower bound for the minim...

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Bibliographic Details
Published in:Designs, codes, and cryptography Vol. 92; no. 10; pp. 3033 - 3048
Main Author: Navarro, Horacio
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2024
Springer Nature B.V
Subjects:
Algebra
Codes
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Fields (mathematics)
Geometry
Linear codes
Linearization
Lower bounds
Linearized function fields
GAG codes
14H05
Riemann–Roch spaces
AG codes
94B27
Algebraic curves
11G20
ISSN:0925-1022, 1573-7586
Online Access:Get full text
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Summary:Several applications of function fields over finite fields, or equivalently, algebraic curves over finite fields, require computing bases for Riemann–Roch spaces. In this paper, we determine explicit bases for Riemann–Roch spaces of linearized function fields, and we give a lower bound for the minimum distance of generalized algebraic geometry codes. As a consequence, we construct generalized algebraic geometry codes with good parameters.
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ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-024-01426-6