On an uncertainty principle for small index subgroups of finite fields

Diego Fernando Díaz Padilla; Jesús Alonso Ochoa Arango

On an uncertainty principle for small index subgroups of finite fields

Number Theory 2024-05-27 v2 Information Theory Commutative Algebra Group Theory math.IT

Authors: Diego Fernando Díaz Padilla , Jesús Alonso Ochoa Arango

Abstract

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

Keywords

uncertainty principle finite fields subgroups compressed fourier matrix nonvanishing minors characters

Cite

@article{arxiv.2310.09992,
  title  = {On an uncertainty principle for small index subgroups of finite fields},
  author = {Diego Fernando Díaz Padilla and Jesús Alonso Ochoa Arango},
  journal= {arXiv preprint arXiv:2310.09992},
  year   = {2024}
}

Comments

9 pages, Comments wellcome. Minor changes

On an uncertainty principle for small index subgroups of finite fields

Abstract

Keywords

Cite

Comments

Related papers