On the Covering Radius of Long 5-ary BCH Codes with Minimum Distance 7

1997 ◽  
Vol 8 (5) ◽  
pp. 403-410
Author(s):  
Y. Kaipainen ◽  
K. Suominen
Keyword(s):  
Minimum Distance ◽  
Covering Radius ◽  
Bch Codes

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

scholarly journals A new efficient way based on special stabilizer multiplier permutations to attack the hardness of the minimum weight search problem for large BCH codes

2019 ◽  
Vol 9 (2) ◽  
pp. 1232
Author(s):  
Issam Abderrahman Joundan ◽  
Said Nouh ◽  
Mohamed Azouazi ◽  
Abdelwahed Namir
Keyword(s):  
Coding Theory ◽  
Minimum Distance ◽  
Minimum Weight ◽  
Error Correcting Codes ◽  
Bch Codes ◽  
Search Problem ◽  
Public Key Cryptosystems ◽  
True Value ◽  
Efficient Scheme ◽  
Minimum Distances

<span>BCH codes represent an important class of cyclic error-correcting codes; their minimum distances are known only for some cases and remains an open NP-Hard problem in coding theory especially for large lengths. This paper presents an efficient scheme ZSSMP (Zimmermann Special Stabilizer Multiplier Permutation) to find the true value of the minimum distance for many large BCH codes. The proposed method consists in searching a codeword having the minimum weight by Zimmermann algorithm in the sub codes fixed by special stabilizer multiplier permutations. These few sub codes had very small dimensions compared to the dimension of the considered code itself and therefore the search of a codeword of global minimum weight is simplified in terms of run time complexity.  ZSSMP is validated on all BCH codes of length 255 for which it gives the exact value of the minimum distance. For BCH codes of length 511, the proposed technique passes considerably the famous known powerful scheme of Canteaut and Chabaud used to attack the public-key cryptosystems based on codes. ZSSMP is very rapid and allows catching the smallest weight codewords in few seconds. By exploiting the efficiency and the quickness of ZSSMP, the true minimum distances and consequently the error correcting capability of all the set of 165 BCH codes of length up to 1023 are determined except the two cases of the BCH(511,148) and BCH(511,259) codes. The comparison of ZSSMP with other powerful methods proves its quality for attacking the hardness of minimum weight search problem at least for the codes studied in this paper.</span>

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.

scholarly journals Bounds on the minimum distance of the duals of BCH codes

1996 ◽  
Vol 42 (4) ◽  
pp. 1257-1260 ◽  
Author(s):  
D. Augot ◽  
F. Levy-dit-Vehel
Keyword(s):  
Minimum Distance ◽  
Bch Codes

On Cosets of Weight 4 of Binary BCH Codes with Minimum Distance 8 and Exponential Sums

2005 ◽  
Vol 41 (4) ◽  
pp. 331-348 ◽  
Author(s):  
V. A. Zinoviev ◽  
T. Helleseth ◽  
P. Charpin
Keyword(s):  
Minimum Distance ◽  
Exponential Sums ◽  
Bch Codes

scholarly journals On BCH split metacyclic codes

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Angelot Behajaina
Keyword(s):  
Lower Bounds ◽  
Minimum Distance ◽  
Bch Codes ◽  
Semidirect Products ◽  
Cyclic Groups ◽  
Dihedral Codes

<p style='text-indent:20px;'>Recently, Borello and Jamous have investigated some lower bounds on the dimension and minimum distance for dihedral codes, in analogy with the theory of BCH codes. In this paper, we extend some of their results to split metacyclic codes, that is, codes over semidirect products of cyclic groups.</p>

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