New efficient scheme based on reduction of the dimension in the multiple impulse method to find the minimum distance of linear codes

TitreNew efficient scheme based on reduction of the dimension in the multiple impulse method to find the minimum distance of linear codes
Publication TypeJournal Article
Year of Publication2016
AuthorsNouh, Sa, Joundan, IAa, Aylaj, Bb, Belkasmi, Mc, Namir, Aa
JournalInternational Review on Computers and Software
Volume11
Pagination742-751
Abstract

In order to find a minimum weight codeword in a linear code, the Multiple Impulse Method uses the Ordered Statistics Decoder of order 3 having a complexity which increases with the code dimension. This paper presents an important improvement of this method by finding a sub code of C of small dimension containing a lowest weight codeword. In the case of Binary Extended Quadratic Residue codes, the proposed technique consists on finding a self invertible permutation σ from the projective special linear group and searching a codeword having the minimum weight in the sub code fixed by σ. The proposed technique gives the exact value of the minimum distance for all binary quadratic residue codes of length less than 223 by using the Multiple Impulse Method on the sub codes in less than one second. For lengths more than 223, the obtained results prove the height capacity of the proposed technique to find the lowest weight in less time. The proposed idea is generalized for BCH codes and it has permits to find the true value of the minimum distance for some codes of lengths 1023 and 2047. The proposed methods performed very well in comparison to previously known results. © 2016 Praise Worthy Prize S.r.l. - All rights reserved.

URLhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85006717110&doi=10.15866%2firecos.v11i9.9702&partnerID=40&md5=0cb2c7691fda83c0ef9764a93095e64c
DOI10.15866/irecos.v11i9.9702
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