A new algorithm for finding minimum-weight words in a linear code: application to McEliece's cryptosystem and to BCH codes of length 511

2002 ◽  
Author(s):  
A. Canteaut ◽  
F. Chaband
Keyword(s):  
Linear Code ◽  
Minimum Weight ◽  
Bch Codes

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 Studying the locator polynomials of minimum weight codewords of BCH codes

1992 ◽  
Vol 38 (3) ◽  
pp. 960-973 ◽  
Author(s):  
D. Augot ◽  
P. Charpin ◽  
N. Sendrier
Keyword(s):  
Minimum Weight ◽  
Bch Codes

Estimates for distribution of the minimal distance of a random linear code

2016 ◽  
Vol 26 (4) ◽  
Author(s):  
Viktor A. Kopyttcev ◽  
Vladimir G. Mikhailov
Keyword(s):  
Distribution Function ◽  
Finite Field ◽  
Linear Code ◽  
Minimum Distance ◽  
Minimum Weight ◽  
Minimal Distance ◽  
Asymptotic Estimates

AbstractThe distribution function of the minimum distance (the minimum weight of nonzero codewords) of a random linear code over a finite field is studied. Expicit bounds in the form of inequalities and asymptotic estimates for this distribution function are obtained.

scholarly journals An Extension of the Brouwer–Zimmermann Algorithm for Calculating the Minimum Weight of a Linear Code

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2354
Author(s):  
Stefka Bouyuklieva ◽  
Iliya Bouyukliev
Keyword(s):  
Finite Field ◽  
Linear Code ◽  
Software Package ◽  
Minimum Weight

A modification of the Brouwer–Zimmermann algorithm for calculating the minimum weight of a linear code over a finite field is presented. The aim was to reduce the number of codewords for consideration. The reduction is significant in cases where the length of a code is not divisible by its dimensions. The proposed algorithm can also be used to find all codewords of weight less than a given constant. The algorithm is implemented in the software package QextNewEdition.

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