Download e-book for iPad: Applied algebra, algebraic algorithms and error-correcting by Serdar Boztas, Hsiao-feng Lu

By Serdar Boztas, Hsiao-feng Lu

ISBN-10: 3540772235

ISBN-13: 9783540772231

This e-book constitutes the refereed court cases of the seventeenth foreign Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-17, held in Bangalore, India, in December 2007.

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

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

Sample text

J. Bernstein and T. Lange √ √ the points (0 : ± d : 1) and (± d : 0 : 1), without mapping to an Edwards curve. We restricted to points (X1 : Y1 : Z1 ) with X1 Y1 Z1 = 0 to maintain the link with Edwards curves and the Edwards addition law. 4 Addition Obtaining more efficient addition formulas was our main goal in investigating inverted Edwards coordinates. Inspecting the addition formulas in [4, Section 4] one notices that the computations of the resulting X3 and Y3 each involve a multiplication by Z1 Z2 .

This leads to the following natural questions: ) 1. Can we achieve the list decoding capacity for smaller alphabets, say for 2Ω(1/ε) (for which the list decoding capacity as we saw in the introduction is 1 − R)? 2. Can we achieve list decoding capacity for codes over fixed alphabet sizes, for example, binary codes? The best known answers to both of the questions above use the notion of code concatenation and Theorem 2. We now digress for a bit to talk about concatenated codes (and along the way motivate why list recovery is an important algorithmic task).

For this paper let L denote F2n , the finite field with 2n elements. Let tr denote the trace map from L to F2 . We usually use the inner product x, y = tr(xy) when Vn = L. Research supported by the Claude Shannon Institute, Science Foundation Ireland Grant 06/MI/006. S. F. ): AAECC 2007, LNCS 4851, pp. 28–37, 2007. c Springer-Verlag Berlin Heidelberg 2007 Spectra of Boolean Functions, Subspaces of Matrices 29 For a function f : L −→ L the formula for f becomes (−1)tr(bf (x)+ax) . f (a, b) := (1) x∈L In this context, f is almost bent if and only if each of the Boolean functions tr(bf (x)) is near-bent, for all b ∈ L, b = 0.

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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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