Applied algebra, algebraic algorithms and error-correcting by Serdar Boztas, Hsiao-feng Lu PDF

By Serdar Boztas, Hsiao-feng Lu

ISBN-10: 3540772235

ISBN-13: 9783540772231

This booklet constitutes the refereed complaints of the seventeenth overseas Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-17, held in Bangalore, India, in December 2007.

The 33 revised complete papers provided including eight invited papers have been rigorously reviewed and chosen from sixty one submissions. one of the topics addressed are block codes, together with list-decoding algorithms; algebra and codes: jewelry, fields, algebraic geometry codes; algebra: jewelry and fields, polynomials, diversifications, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.

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Extra info for Applied algebra, algebraic algorithms and error-correcting codes: 17th international symposium, AAECC-17, Bangalore, India, December 16-20, 2007: proceedings

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In other words, the maximum fraction of errors that can be S. F. ): AAECC 2007, LNCS 4851, pp. 38–46, 2007. c Springer-Verlag Berlin Heidelberg 2007 Efficient List Decoding of Explicit Codes with Optimal Redundancy 39 corrected (via list decoding) using a rate R code (or the list decoding capacity), is given by the trade-off Hq−1 (1 − R). For q = 2Ω(1/ε) , Hq−1 (1 − R) 1 − R − ε (cf. [13]). In other words, for large enough alphabets, the list decoding capacity is ρcap (R) = 1 − R. Now is a good time to compare the list decoding capacity with what can be achieved with “usual” notion of decoding for the worst-case noise model (called unique decoding), where the decoder has to always output the transmitted word.

3] that if d is not a square in k then the Edwards addition law has an even more attractive feature: it is complete. This means that there are no points (x1 , y1 ), (x2 , y2 ) on the curve where the denominators vanish; the Edwards addition law produces the correct output for every pair of input points. The neutral element (0, 1) does not cause any trouble. The Edwards curve has two singularities at infinity, corresponding to four points √ on the desingularization of the curve; but those four points are defined over k( d), not over k.

Concatenated codes are constructed from two different codes that are defined over alphadef bets of different sizes. Say we are interested in a code over [q] = {0, 1, . . , q − 1} (in this section, we will think of q 2 as being a fixed constant). Then the outer code Cout is defined over [Q], where Q = q k for some positive integer k. The second code, called the inner code is defined over [q] and is of dimension k (Note that the message space of Cin and the alphabet of Cout have the same size). The concatenated code, denoted by C = Cout ◦ Cin , is defined as follows.

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Applied algebra, algebraic algorithms and error-correcting codes: 17th international symposium, AAECC-17, Bangalore, India, December 16-20, 2007: proceedings by Serdar Boztas, Hsiao-feng Lu

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