Abstract
The paper examines some of the properties of some multi-parameter burst error correcting cyclic codes. Some conjectures given earlier are proven, and the codes are shown to be equivalent to single parity check product codes (Gilbert codes) or shortened Gilbert codes. The codes are shown to correct arbitrary burst shapes, and design algorithms are included.
Résumé
Cet article étudie certaines propriétés des codes cycliques multi-paramètres concernant la correction d’erreurs par lots. Des conjectures avancées précédement sont démontreés ainsi que l’équivalence entre ces codes et les codes de Gilbert (éventuellement raccourcis). On montre que ces codes peuvent corriger des erreurs de répartition arbitraires et des algorithms de résolution sont donnés.
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References
Bahl, L. R. and R. T. Chien: Single and multi-burst correcting properties of a class of cyclic product codes, IEEE Trans., IT-17 (1971), 594–600.
Farrell, P. G.: An introduction to array error control codes, in: CISM Courses and Lectures 313 Geometries, Codes and Cryptography (Ed. G. Longo et al),Springer-Verlag, Wien, 1990, 101–128.
Gilbert, E. N.: A problem in binary encoding, Proc. of Symposia in Applied Maths., 10—Combinatorial Theory, American. Math. Soc., (1960), 291–297.
Olcayto, E. and T. Lesz: Class of linear cyclic block codes for burst errors occuring in one-,two-and three-dimensional channels, IEE Proc. Part F, 130 (5) (1983), 468–475.
Olcayto, E. and T. Lesz: Simple cyclic codes for burst errors, IEE Proc. Part F, 131 (2) (1984), 153–155.
Olcayto, E. and A. R. Birse: Split syndrome burst error correcting codes for one-dimensional channels, IEE Proc. Part F, 134 (4) (1987), pp 373–376.
Olcayto, E. and A. R. Birse: New class of cyclic, random and burst error correcting codes, Proceedings of AAECC-5, Springer-Verlag, 1988, 357–368.
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© 1993 Springer-Verlag Wien
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Olcayto, E., Irvine, J.M. (1993). Multi-Parameter Cyclic Codes for Burst and Random Error Correction. In: Camion, P., Charpin, P., Harari, S. (eds) Eurocode ’92. International Centre for Mechanical Sciences, vol 339. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2786-5_22
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DOI: https://doi.org/10.1007/978-3-7091-2786-5_22
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82519-8
Online ISBN: 978-3-7091-2786-5
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