Bulygin, Stanislav ; Pellikaan, Ruud (2009)
Bounded distance decoding of linear error-correcting codes with Gröbner bases.
In: Journal of Symbolic Computation, 44 (12)
doi: 10.1016/j.jsc.2007.12.003
Artikel, Bibliographie
Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2009 |
| Autor(en): | Bulygin, Stanislav ; Pellikaan, Ruud |
| Art des Eintrags: | Bibliographie |
| Titel: | Bounded distance decoding of linear error-correcting codes with Gröbner bases |
| Sprache: | Englisch |
| Publikationsjahr: | Dezember 2009 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Journal of Symbolic Computation |
| Jahrgang/Volume einer Zeitschrift: | 44 |
| (Heft-)Nummer: | 12 |
| DOI: | 10.1016/j.jsc.2007.12.003 |
| Kurzbeschreibung (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. |
| Freie Schlagworte: | Secure Data;Decoding; Gröbner basis; Linear code; Minimum distance; Syndrome decoding; System of polynomial equations |
| ID-Nummer: | TUD-CS-2010-0001 |
| Fachbereich(e)/-gebiet(e): | LOEWE LOEWE > LOEWE-Zentren LOEWE > LOEWE-Zentren > CASED – Center for Advanced Security Research Darmstadt |
| Hinterlegungsdatum: | 30 Dez 2016 20:23 |
| Letzte Änderung: | 01 Nov 2020 18:32 |
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