On an uncertainty principle for small index subgroups of finite fields

Jesus Alonso Ochoa Arango; Diego Fernando Díaz Padilla

doi:10.1515/math-2025-0178

On an uncertainty principle for small index subgroups of finite fields

Jesus Alonso Ochoa Arango, Diego Fernando Díaz Padilla

University of Southern California

Producción: Contribución a una revista › Artículo › revisión exhaustiva

Resumen

In this article, we continue the study of the nonvanishing minors property initiated by Garcia, Karaali, and Katz, for the compressed Fourier matrix attached to a subgroup H H of the multiplicative group of a finite field F q {{\mathbb{F}}}_{q} and a character χ \chi defined over H H. Here, we provide a characterization of this aforementioned property for symmetries arising from an index-3 subgroup H H and a nontrivial character χ \chi.

Idioma original	Inglés
Número de artículo	20250178
Páginas (desde-hasta)	1-8
Número de páginas	8
Publicación	Open Mathematics
Volumen	23
N.º	1
DOI	https://doi.org/10.1515/math-2025-0178
Estado	Publicada - 02 sep. 2025

Palabras clave

Fourier transform
DFT matrix
compressed Fourier transform
nonvanishing minors
uncertainty principle
Gauss sum
finite field
group character

ODS de las Naciones Unidas

Este resultado contribuye a los siguientes Objetivos de Desarrollo Sostenible

Acceder al documento

10.1515/math-2025-0178

Otros archivos y enlaces

10.1515_math-2025-0178

Enlace a la publicación en Scopus

Lie bialgebra structures over the Lie algebra of truncated polynomials
Ochoa Arango, J. A. (Investigador principal)
26/10/20 → 25/04/22
Proyecto: Investigación

Citar esto

@article{3d3ec75357b843429b6ab488631839c4,

title = "On an uncertainty principle for small index subgroups of finite fields",

abstract = "In this article, we continue the study of the nonvanishing minors property initiated by Garcia, Karaali, and Katz, for the compressed Fourier matrix attached to a subgroup H H of the multiplicative group of a finite field F q \{\{\textbackslash{}mathbb\{F\}\}\}\_\{q\} and a character χ \textbackslash{}chi defined over H H. Here, we provide a characterization of this aforementioned property for symmetries arising from an index-3 subgroup H H and a nontrivial character χ \textbackslash{}chi.",

keywords = "Fourier transform, DFT matrix, compressed Fourier transform, nonvanishing minors, uncertainty principle, Gauss sum, finite field, group character",

author = "\{Ochoa Arango\}, \{Jesus Alonso\} and \{D{\'i}az Padilla\}, \{Diego Fernando\}",

note = "Publisher Copyright: {\textcopyright} 2025 the author(s), published by De Gruyter.",

year = "2025",

month = sep,

day = "2",

doi = "10.1515/math-2025-0178",

language = "English",

volume = "23",

pages = "1--8",

journal = "Open Mathematics",

issn = "2391-5455",

number = "1",

}

TY - JOUR

T1 - On an uncertainty principle for small index subgroups of finite fields

AU - Ochoa Arango, Jesus Alonso

AU - Díaz Padilla, Diego Fernando

PY - 2025/9/2

Y1 - 2025/9/2

N2 - In this article, we continue the study of the nonvanishing minors property initiated by Garcia, Karaali, and Katz, for the compressed Fourier matrix attached to a subgroup H H of the multiplicative group of a finite field F q {{\mathbb{F}}}_{q} and a character χ \chi defined over H H. Here, we provide a characterization of this aforementioned property for symmetries arising from an index-3 subgroup H H and a nontrivial character χ \chi.

AB - In this article, we continue the study of the nonvanishing minors property initiated by Garcia, Karaali, and Katz, for the compressed Fourier matrix attached to a subgroup H H of the multiplicative group of a finite field F q {{\mathbb{F}}}_{q} and a character χ \chi defined over H H. Here, we provide a characterization of this aforementioned property for symmetries arising from an index-3 subgroup H H and a nontrivial character χ \chi.

KW - Fourier transform

KW - DFT matrix

KW - compressed Fourier transform

KW - nonvanishing minors

KW - uncertainty principle

KW - Gauss sum

KW - finite field

KW - group character

UR - https://www.scopus.com/pages/publications/105014943231

U2 - 10.1515/math-2025-0178

DO - 10.1515/math-2025-0178

M3 - Article

SN - 2391-5455

VL - 23

SP - 1

EP - 8

JO - Open Mathematics

JF - Open Mathematics

IS - 1

M1 - 20250178

ER -

On an uncertainty principle for small index subgroups of finite fields

Resumen

Palabras clave

ODS de las Naciones Unidas

Acceder al documento

Otros archivos y enlaces

Proyectos

Lie bialgebra structures over the Lie algebra of truncated polynomials

Citar esto