TU Darmstadt / ULB / TUbiblio

Bounded distance decoding of linear error-correcting codes with Gröbner bases

Bulygin, Stanislav and Pellikaan, Ruud :
Bounded distance decoding of linear error-correcting codes with Gröbner bases.
In: Journal of Symbolic Computation, Special Issue "Gröbner Ba (Issue 12) pp. 1626-1643.
[Article] , (2009)

Abstract

The problem of bounded distance decoding of arbitrary linear codes using Gröbner bases is addressed. A new method is proposed, which is based on reducing an initial decoding problem to solving a certain system of polynomial equations over a finite field. The peculiarity of this system is that, when we want to decode up to half the minimum distance, it has a unique solution even over the algebraic closure of the considered finite field, although field equations are not added. The equations in the system have degree at most 2. As our experiments suggest, our method is much faster than the one of Fitzgerald–Lax. It is also shown via experiments that the proposed approach in some range of parameters is superior to the generic syndrome decoding.

Item Type: Article
Erschienen: 2009
Creators: Bulygin, Stanislav and Pellikaan, Ruud
Title: Bounded distance decoding of linear error-correcting codes with Gröbner bases
Language: ["languages_typename_1" not defined]
Abstract:

The problem of bounded distance decoding of arbitrary linear codes using Gröbner bases is addressed. A new method is proposed, which is based on reducing an initial decoding problem to solving a certain system of polynomial equations over a finite field. The peculiarity of this system is that, when we want to decode up to half the minimum distance, it has a unique solution even over the algebraic closure of the considered finite field, although field equations are not added. The equations in the system have degree at most 2. As our experiments suggest, our method is much faster than the one of Fitzgerald–Lax. It is also shown via experiments that the proposed approach in some range of parameters is superior to the generic syndrome decoding.

Journal or Publication Title: Journal of Symbolic Computation
Volume: Special Issue "Gröbner Ba
Number: Issue 12
Uncontrolled Keywords: Secure Data;Decoding; Gröbner basis; Linear code; Minimum distance; Syndrome decoding; System of polynomial equations
Divisions: LOEWE > LOEWE-Zentren > CASED – Center for Advanced Security Research Darmstadt
LOEWE > LOEWE-Zentren
LOEWE
Date Deposited: 30 Dec 2016 20:23
DOI: 10.1016/j.jsc.2007.12.003
Identification Number: TUD-CS-2010-0001
Export:

Optionen (nur für Redakteure)

View Item View Item