Abstract
The content of these notes is a tentative survey of the results recently obtained concerning one of the most attractive methods known for decoding linear block codes. The material is divided into four sections, each followed by a list of references. The first serves as an introduction to the subject. The second section deals with geometric codes, which constitutes the largest class of threshold — decodable codes. The third section is concerned with the generalized Reed-Muller codes, which provide the setting for studying geometric codes. Finally, in section four, an example is given of the improvements of Rudolph’s method which can be obtained from the combinatorial structure of a code.
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References
Assmus, E.F., Jr., and H.F. Mattson, Jr., On tactical configurations and error-correcting codes, J. Combin. Theory, 2 (1967), 243–257.
Goethals, J.M, On the Golay perfect binary code, J. Combin. Theory, 11 (1971), 178–166.
Goethals, J.M., On t-designs and threshold decoding, Univ. North Carolina, Inst. Statist. Mimeo Ser. No. 600. 29 (1970).
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© 1975 Springer-Verlag Wien
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Goethals, J.M. (1975). Threshold Decoding. In: Longo, G. (eds) Coding and Complexity. International Centre for Mechanical Sciences, vol 216. Springer, Vienna. https://doi.org/10.1007/978-3-7091-3008-7_2
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DOI: https://doi.org/10.1007/978-3-7091-3008-7_2
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81341-6
Online ISBN: 978-3-7091-3008-7
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