scholarly journals Locally Decodable Codes from Nice Subsets of Finite Fields and Prime Factors of Mersenne Numbers

2009 ◽  
Vol 38 (5) ◽  
pp. 1952-1969 ◽  
Author(s):  
Kiran S. Kedlaya ◽  
Sergey Yekhanin
Keyword(s):  
Finite Fields ◽  
Mersenne Numbers ◽  
Locally Decodable Codes ◽  
Prime Factors ◽  
Locally Decodable

scholarly journals High-entropy dual functions over finite fields and locally decodable codes

2021 ◽  
Vol 9 ◽  
Author(s):  
Jop Briët ◽  
Farrokh Labib
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Multiple Correlation ◽  
High Entropy ◽  
Polynomial Phase ◽  
Locally Decodable Codes ◽  
Phase Functions ◽  
Correlation Sequences ◽  
Locally Decodable ◽  
Dual Functions

Abstract 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.

scholarly journals On the Capacity of Locally Decodable Codes

2020 ◽  
Vol 66 (10) ◽  
pp. 6566-6579
Author(s):  
Hua Sun ◽  
Syed Ali Jafar
Keyword(s):  
Locally Decodable Codes ◽  
Locally Decodable
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