Bulygin, Stanislav ; Pellikaan, Ruud
Hrsg.: Woungang, Isaac ; Misra, Sudip ; Misra, Subhas Chandra (2010)
Decoding and Finding the Minimum Distance with Gröbner Bases: History and New Insights.
In: Selected Topics in Information and Coding Theory
Buchkapitel, Bibliographie
Kurzbeschreibung (Abstract)
In this chapter we discuss decoding techniques and finding the minimum distance of linear codes with the use of Gröbner bases. First we give a historical overview of decoding cyclic codes via solving systems of polynomial equations over finite fields. In particular we mention papers of Cooper, Reed, Chen, Helleseth, Truong, Augot, Mora, Sala and others. Some structural theorems that use Gröbner bases in this context are presented. After that we shift to the general situation of arbitrary linear codes. We give an overview of approaches of Fitzgerald and Lax. Then we introduce our method of decoding linear codes that reduces this problem to solving a system of quadratic equations. We discuss open problems and future research possibilities.
| Typ des Eintrags: | Buchkapitel |
|---|---|
| Erschienen: | 2010 |
| Herausgeber: | Woungang, Isaac ; Misra, Sudip ; Misra, Subhas Chandra |
| Autor(en): | Bulygin, Stanislav ; Pellikaan, Ruud |
| Art des Eintrags: | Bibliographie |
| Titel: | Decoding and Finding the Minimum Distance with Gröbner Bases: History and New Insights |
| Sprache: | Englisch |
| Publikationsjahr: | März 2010 |
| Verlag: | World Scientific |
| Buchtitel: | Selected Topics in Information and Coding Theory |
| Kurzbeschreibung (Abstract): | In this chapter we discuss decoding techniques and finding the minimum distance of linear codes with the use of Gröbner bases. First we give a historical overview of decoding cyclic codes via solving systems of polynomial equations over finite fields. In particular we mention papers of Cooper, Reed, Chen, Helleseth, Truong, Augot, Mora, Sala and others. Some structural theorems that use Gröbner bases in this context are presented. After that we shift to the general situation of arbitrary linear codes. We give an overview of approaches of Fitzgerald and Lax. Then we introduce our method of decoding linear codes that reduces this problem to solving a system of quadratic equations. We discuss open problems and future research possibilities. |
| Freie Schlagworte: | Secure Data |
| ID-Nummer: | TUD-CS-2009-0136 |
| Fachbereich(e)/-gebiet(e): | LOEWE > LOEWE-Zentren > CASED – Center for Advanced Security Research Darmstadt LOEWE > LOEWE-Zentren LOEWE |
| Hinterlegungsdatum: | 30 Dez 2016 20:23 |
| Letzte Änderung: | 17 Mai 2018 13:02 |
| PPN: | |
| Export: | |
| Suche nach Titel in: | TUfind oder in Google |
 |
Frage zum Eintrag |
Optionen (nur für Redakteure)
 |
Redaktionelle Details anzeigen |
Drucken
Impressum