New lower bounds for the minimum distance of generalized algebraic geometry codes

2013 ◽  
Vol 217 (6) ◽  
pp. 1164-1172 ◽  
Author(s):  
Alberto Picone
Keyword(s):  
Algebraic Geometry ◽  
Lower Bounds ◽  
Minimum Distance ◽  
Algebraic Geometry Codes

A comparison between Suzuki invariant code and one-point Hermitian code

2021 ◽  
pp. 2150104
Author(s):  
Abdulla Eid
Keyword(s):  
Algebraic Geometry ◽  
Minimum Distance ◽  
Algebraic Curves ◽  
Automorphism Groups ◽  
Algebraic Geometry Codes ◽  
Hermitian Codes ◽  
Relative Minimum ◽  
Minimum Distances ◽  
Hermitian Code

In this paper we compare the performance of two algebraic geometry codes (Suzuki and Hermitian codes) constructed using maximal algebraic curves over [Formula: see text] with large automorphism groups by choosing specific divisors. We discuss their parameters, compare the rate of these codes as well as their relative minimum distances, and we show that both codes are asymptotically good in terms of the rate which is in contrast to their behavior in terms of the relative minimum distance.

scholarly journals Further improvements on the designed minimum distance of algebraic geometry codes

2009 ◽  
Vol 213 (1) ◽  
pp. 87-97 ◽  
Author(s):  
Cem Güneri ◽  
Henning Stichtenoth ◽  
İhsan Taşkın
Keyword(s):  
Algebraic Geometry ◽  
Minimum Distance ◽  
Algebraic Geometry Codes

scholarly journals On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups

2018 ◽  
Vol 86 (12) ◽  
pp. 2893-2916 ◽  
Author(s):  
José I. Farrán ◽  
Pedro A. García-Sánchez ◽  
Benjamín A. Heredia
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Geometry Codes ◽  
Rao Distance ◽  
Arf Semigroups

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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