Read e-book online Applied Algebra, Algebraic Algorithms and Error-Correcting PDF

By G. David Forney Jr. (auth.), Marc Fossorier, Hideki Imai, Shu Lin, Alain Poli (eds.)

ISBN-10: 3540467963

ISBN-13: 9783540467960

ISBN-10: 3540667237

ISBN-13: 9783540667230

This booklet constitutes the refereed complaints of the nineteenth foreign Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, held in Honolulu, Hawaii, united states in November 1999.
The forty two revised complete papers awarded including six invited survey papers have been conscientiously reviewed and chosen from a complete of 86 submissions. The papers are geared up in sections on codes and iterative interpreting, mathematics, graphs and matrices, block codes, jewelry and fields, deciphering equipment, code building, algebraic curves, cryptography, codes and interpreting, convolutional codes, designs, interpreting of block codes, modulation and codes, Gröbner bases and AG codes, and polynomials.

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Additional info for Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th International Symposium, AAECC-13 Honolulu, Hawaii, USA, November 15–19, 1999 Proceedings

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The span of all formal sums g∈G ag g with complex coefficients. The multiplication in G extends to the so-called convolution in CG: ag g · g∈G ag bg−1 k k. bh h = h∈G k∈G g∈G Marc Fossorier et al. ): AAECC-13, LNCS 1719, pp. 29–42, 1999. c Springer-Verlag Berlin Heidelberg 1999 30 Michael Clausen and Meinard M¨ uller In this way, CG becomes a C-algebra, the so-called group algebra of G over C. For example, if G = Cn = X | X n = 1 is the cyclic group of order n, then CG can be identified with the polynomial ring C[X] modulo the ideal generated by X n − 1.

The multiplication in G extends to the so-called convolution in CG: ag g · g∈G ag bg−1 k k. bh h = h∈G k∈G g∈G Marc Fossorier et al. ): AAECC-13, LNCS 1719, pp. 29–42, 1999. c Springer-Verlag Berlin Heidelberg 1999 30 Michael Clausen and Meinard M¨ uller In this way, CG becomes a C-algebra, the so-called group algebra of G over C. For example, if G = Cn = X | X n = 1 is the cyclic group of order n, then CG can be identified with the polynomial ring C[X] modulo the ideal generated by X n − 1. In this case, convolution in CG means ordinary polynomial multiplication modulo the relation X n = 1.

Xn ] can be written using Inclusion–Exclusion as follows. For I ⊆ {1, 2, . . , r} let mI denote the least common multiple of {mi : i ∈ I}. Proposition 2. The Hilbert series of M equals {xi11 xi22 · · · xinn ∈ M} 1 = n i=1 (1 − xi ) (−1)|I| · mI . 1) I⊆{1,2,... ,r} Unfortunately this formula is useless for our problem (i), because the number of summands is an exponential function in r. But almost all summands cancel. In this section we show that for n = 3 the true number of summands in the numerator of the Hilbert series of M is a linear function in r.

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th International Symposium, AAECC-13 Honolulu, Hawaii, USA, November 15–19, 1999 Proceedings by G. David Forney Jr. (auth.), Marc Fossorier, Hideki Imai, Shu Lin, Alain Poli (eds.)


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