F. J. MacWilliams and N.J. A. Sloane, The Theor!l of Error-Correctitzg Codes, North-Holland, New York, 1977.  Home/Search   Document Not in Database   Summary   Related Articles

....[9] 10] These applications also fall into the category of erasure channel coding. 2 Diversity Coding We assume that the reader is familiar with the theory of finite fields. For more information on this subject we refer the reader to one of the standard texts on the subject such as [11] or [12], or to [13] for a summary. In Section 2.1 we present a minimum set of information on linear coding theory to introduce notation and nomenclature, and to enable the reader to follow the discussion in the rest of the section. Then, using this background, we describe two methods of diversity coding ....

....above can also correct 5 erasures with 5 parity symbols, and are in systematic form, they are also MDS codes, as were those described previously. Codes whose parity check matrices are equivalent to a Fourier matrix such as the ones described above belong to the class of Reed Solomon codes [12]. There exist fast methods for calculating error magnitudes for Reed Solomon codes, such as the Forhey algorithm [11, p. 183] or the frequency domain techniques [11, p. 256] A slight reduction in field size can be obtained by using extended Reed Solomon codes [12, p. 323] making the field size ....

F. J. MacWilliams and N.J. A. Sloane, The Theor!l of Error-Correctitzg Codes, North-Holland, New York, 1977.

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