By Venkatesan Guruswami (auth.), Serdar Boztaş, Hsiao-Feng (Francis) Lu (eds.)

ISBN-10: 3540772235

ISBN-13: 9783540772231

ISBN-10: 3540772243

ISBN-13: 9783540772248

This e-book constitutes the refereed lawsuits 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 8 invited papers have been rigorously 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, diversifications, 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

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Otherwise inserting Z1 /X1 for x1 and x2 and Z1 /Y1 for y1 and y2 in the Edwards addition law we obtain 2(x1 , y1 ) = 2X1 Y1 Z12 (X12 − Y12 )Z12 , X12 Y12 + dZ14 X12 Y12 − dZ14 = X2 − Y 2 2X1 Y1 , 2 1 2 1 2 2 X1 + Y1 X1 + Y1 − 2dZ12 . In the second equality we have used the curve equation to replace X12 Y12 by (X12 + Y12 )Z12 − dZ14 , and then cancelled Z12 , reducing the overall degree of the formulas to 4. The resulting coordinates are X3 = (X12 + Y12 )(X12 − Y12 ) Y3 = 2X1 Y1 (X12 + Y12 − 2dZ12 ) Z3 = 2X1 Y1 (X12 − Y12 ).

Dillon’s result states that the function f (x, y) = n g(xy 2 −2 ) is bent on K × K (actually the result is more general, concerning n partial spread bent functions). Note that g(xy 2 −2 ) = g(x/y) if y = 0. In K × K let Ha denote the line {(x, ax) : x ∈ K} and let H∞ = {(0, y) : y ∈ K}. These 2t + 1 lines intersect pairwise in (0, 0) and partition K × K. The linear span of any two of these lines is K × K. Spectra of Boolean Functions, Subspaces of Matrices 35 Let H be a hyperplane in K × K. We must show that the Fourier transform of f |H takes values 0, ±2t.

The connection 30 G. McGuire goes through bilinear forms. This work is all implicit in Delsarte and Goethals [4]. They translate the results on bilinear forms into results in coding theory. It is known that such results in coding theory can be translated into results on the Fourier spectra of Boolean functions. We will directly translate results from Boolean functions to results on subspaces of matrices. 1, but we feel that it is useful to directly explain the connection without going through coding theory.

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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 Venkatesan Guruswami (auth.), Serdar Boztaş, Hsiao-Feng (Francis) Lu (eds.)


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