Geodesic
High-entropy dual functions over finite fields and locally decodable codes
Forum of Mathematics, Sigma, Tome 9 (2021)

Voir la notice de l'article provenant de la source Cambridge University Press

We show that for infinitely many primes p there exist dual functions of order k over ${\mathbb{F}}_p^n$ that cannot be approximated in $L_\infty $-distance by polynomial phase functions of degree $k-1$. This answers in the negative a natural finite-field analogue of a problem of Frantzikinakis on $L_\infty $-approximations of dual functions over ${\mathbb{N}}$ (a.k.a. multiple correlation sequences) by nilsequences. 
@article{10_1017_fms_2021_1,
     author = {Jop Bri\"et and Farrokh Labib},
     title = {High-entropy dual functions over finite fields and locally decodable codes},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {9},
     year = {2021},
     doi = {10.1017/fms.2021.1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2021.1/}
}
TY  - JOUR
AU  - Jop Briët
AU  - Farrokh Labib
TI  - High-entropy dual functions over finite fields and locally decodable codes
JO  - Forum of Mathematics, Sigma
PY  - 2021
VL  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2021.1/
DO  - 10.1017/fms.2021.1
LA  - en
ID  - 10_1017_fms_2021_1
ER  - 
%0 Journal Article
%A Jop Briët
%A Farrokh Labib
%T High-entropy dual functions over finite fields and locally decodable codes
%J Forum of Mathematics, Sigma
%D 2021
%V 9
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2021.1/
%R 10.1017/fms.2021.1
%G en
%F 10_1017_fms_2021_1
Jop Briët; Farrokh Labib. High-entropy dual functions over finite fields and locally decodable codes. Forum of Mathematics, Sigma, Tome 9 (2021). doi: 10.1017/fms.2021.1

Cité par Sources :