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

By Serdar Boztas, Hsiao-feng Lu

This e-book constitutes the refereed court cases 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 matters 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

Example text

But our addition formulas still have the advantage of strong unification: they can be used without change to double a point. In Sections 5 and 6 we present formulas for doubling and tripling in inverted Edwards coordinates using only 3M + 4S and 9M + 4S, matching the speeds of standard Edwards coordinates. All of the operation counts stated above assume small curve parameters and disregard the cost of multiplying by a curve parameter. Arbitrary curve parameters cost 1M extra for each addition, each doubling, and each tripling.

Let m 1 be an integer parameter called the folding parameter. For ease of presentation, it will assumed that m divides n = q − 1. Definition 1 (Folded Reed-Solomon Code). The m-folded version of the RS code C, denoted FRSF,γ,m,k , is a code of block length N = n/m over Fm . The encoding of a message f (X), a polynomial over F of degree at most k, has as its j’th symbol, for 0 j < n/m, the m-tuple (f (γ jm ), f (γ jm+1 ), · · · , f (γ jm+m−1 )). In other words, the codewords of C = FRSF,γ,m,k are in one-one correspondence with those of the RS code C and are obtained by bundling together consecutive m-tuple of symbols in codewords of C.

Kasami-Welch Functions on a Hyperplane (submitted) 4. : Alternating Bilinear Forms over GF(q). J. Comb. Th. Ser. A 19, 26–50 (1975) 5. : On the Vanishing of Subspaces of Alternating Bilinear Forms. Linear and Multilinear Algebra 54, 415–428 (2006) 6. : Galois Extensions and Subspaces of Alternating Bilinear Forms with Special Rank Properties (submitted) 7. : Rate-Diversity Tradeoff of Space-Time Codes with Fixed Alphabet and Optimal Constructions for PSK Modulation. IEEE Trans. Inform. Theory 49(10), 2747–2751 (2003) 8.

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