Algebraic decoding of the Zetterberg codes

Algebraic decoding of the Zetterberg codes

The Zetterberg codes are one of the best known families of double-error correcting binary linear codes. Unfortunately, no satisfactory decoding algorithm has been known for them until recently when an algebraic decoding algorithm was described by P. Kallquist (1989). It requires, however, to solve a...

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Veröffentlicht in:IEEE transactions on information theory 1992-09, Vol.38 (5), p.1570-1573
Hauptverfasser: Dodunekov, S.M., Nilsson, J.E.M.
Format: Artikel
Sprache:eng
Schlagworte:
Applied sciences
Coding, codes
Data communication
Decoding
Equations
Exact sciences and technology
Information, signal and communications theory
Linear code
Signal and communications theory
Telecommunications and information theory
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Zusammenfassung:The Zetterberg codes are one of the best known families of double-error correcting binary linear codes. Unfortunately, no satisfactory decoding algorithm has been known for them until recently when an algebraic decoding algorithm was described by P. Kallquist (1989). It requires, however, to solve a quadratic equation in order to decide whether 2 or 3 errors have occurred. A simple criterion is derived to determine whether 1, 2, or 3 errors have occurred when a Zetterberg code is used for data transmission. Based on criterion a new decoding algorithm is proposed which is faster than the known one.< >
ISSN:0018-9448
1557-9654
DOI:10.1109/18.149509