scholarly journals New Covering Radius of Reed-Muller Codes for t-Resilient Functions

2001 ◽  
pp. 75-86 ◽  
Author(s):  
Tetsu Iwata ◽  
Takayuki Yoshiwara ◽  
Kaoru Kurosawa
Keyword(s):  
Covering Radius ◽  
Resilient Functions

New Covering Radius of Reed–Muller Codes for<tex>$t$</tex>-Resilient Functions

2004 ◽  
Vol 50 (3) ◽  
pp. 468-475 ◽  
Author(s):  
K. Kurosawa ◽  
T. Iwata ◽  
T. Yoshiwara
Keyword(s):  
Covering Radius ◽  
Resilient Functions

scholarly journals On extractors and exposure-resilient functions for sublogarithmic entropy

2012 ◽  
Vol 42 (3) ◽  
pp. 386-401 ◽  
Author(s):  
Yakir Reshef ◽  
Salil Vadhan
Keyword(s):  
Resilient Functions

New Results on Codes with Covering Radius 1 and Minimum Distance 2

2005 ◽  
Vol 35 (2) ◽  
pp. 241-250 ◽  
Author(s):  
Patric R. J. �sterg�rd ◽  
J�rn Quistorff ◽  
Alfred Wassermann
Keyword(s):  
Minimum Distance ◽  
Covering Radius

Construction of resilient functions

2005 ◽  
Vol 10 (1) ◽  
pp. 199-202
Author(s):  
Zhang Jie ◽  
Wen Qiao-yan
Keyword(s):  
Resilient Functions

scholarly journals On Mixed Codes with Covering Radius $1$ and Minimum Distance $2$

10.37236/969 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Wolfgang Haas ◽  
Jörn Quistorff
Keyword(s):  
Lower Bounds ◽  
Minimum Distance ◽  
Covering Radius ◽  
Minimal Cardinality ◽  
Finite Sets ◽  
Open Problems ◽  
Latin Rectangle ◽  
Mixed Codes ◽  
Special Case

Let $R$, $S$ and $T$ be finite sets with $|R|=r$, $|S|=s$ and $|T|=t$. A code $C\subset R\times S\times T$ with covering radius $1$ and minimum distance $2$ is closely connected to a certain generalized partial Latin rectangle. We present various constructions of such codes and some lower bounds on their minimal cardinality $K(r,s,t;2)$. These bounds turn out to be best possible in many instances. Focussing on the special case $t=s$ we determine $K(r,s,s;2)$ when $r$ divides $s$, when $r=s-1$, when $s$ is large, relative to $r$, when $r$ is large, relative to $s$, as well as $K(3r,2r,2r;2)$. Some open problems are posed. Finally, a table with bounds on $K(r,s,s;2)$ is given.

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