A Generalized Construction and Improvements on Nonbinary Codes From Goppa Codes

A Generalized Construction and Improvements on Nonbinary Codes From Goppa Codes

We present an efficient construction of extended length Goppa codes. Using this construction, we obtain 78 new nonbinary codes with better minimum distance than the previously known codes with the same length and dimension. The construction is based on the observation that certain Goppa codes can be...

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Veröffentlicht in:IEEE transactions on information theory 2013-11, Vol.59 (11), p.7299-7304
Hauptverfasser: Tomlinson, Martin, Jibril, Mubarak, Tjhai, Cen, Bezzateev, Sergey V., Grassl, Markus, Ahmed, Mohammed Zaki
Format: Artikel
Sprache:eng
Schlagworte:
BCH
Codes
Educational institutions
Electronic mail
error correction
Goppa
Information theory
Parity check codes
Polynomials
Redundancy
Reed-Solomon
Vectors
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Beschreibung
Zusammenfassung:We present an efficient construction of extended length Goppa codes. Using this construction, we obtain 78 new nonbinary codes with better minimum distance than the previously known codes with the same length and dimension. The construction is based on the observation that certain Goppa codes can be seen as BCH codes.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2276626