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

This booklet constitutes the refereed court cases 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 provided including six invited survey papers have been conscientiously reviewed and chosen from a complete of 86 submissions. The papers are equipped in sections on codes and iterative interpreting, mathematics, graphs and matrices, block codes, earrings and fields, deciphering tools, code building, algebraic curves, cryptography, codes and deciphering, convolutional codes, designs, interpreting of block codes, modulation and codes, Gröbner bases and AG codes, and polynomials.

**Read or Download Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th International Symposium, AAECC-13 Honolulu, Hawaii, USA, November 15–19, 1999 Proceedings PDF**

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

**Sample text**

3 and the last example is concerned with a Sylow 2-subgroup of the symmetric group S16. l. t. l. 069 Of course, the ﬁrst three groups are of a very simple nature. However, the running time of the algorithm does not essentially depend on the complexity of the pc-presentation, but mainly on the number and degrees of the irreducible representations constituting the DFT. This is veriﬁed by the more complex example Syl2 (S16 ). Therefore, the actual running times for constructing a monomial DFT of CG reﬂect very well the theoretical result concerning the output length.

Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo codes,” Proc. 1993 IEEE International Conference on Communications, Geneva, Switzerland (May 1993), pp. 1064–1070. 2. D. Divsalar, “A simple tight bound on error probability of block codes with application to turbo codes,” in preparation. 3. D. Divsalar, H. Jin, and R. McEliece. ” Proc. , pp. 201-210. 4. D. Divsalar, S. Dolinar, H. Jin, and R. McEliece, “AWGN Coding Theorems from Ensemble Weight Enumerators,” in preparation.

3) 2. The minimal free resolution of M equals ∂ ∂ ∂ 2 1 0 K[x, y, z]GM −→ K[x, y, z]r −→ M −→ 0 . 4) 3. If M is artinian then the irreducible decomposition equals M xdeg x (mijk ) , y degy (mijk ) , z degz (mijk ) . 5) {i,j,k}∈TM Here M is called artinian if some power of each variable is in M, or equivalently, if the number of standard monomials is ﬁnite. The non-artinian case can be reduced to the artinian case by considering M + xm , y m , z m for m 0. We illustrate Theorem 4 for the generic artinian monomial ideal 1 2 3 4 5 6 7 8 9 10 11 12 x10 , y 10 , z 10 , x8 y 6 z, x9 y 3 z 2 , x4 y 8 z 3 , x7 y 5 z 4 , xy 9 z 5 , x3 y 7 z 6 , x5 y 4 z 7 , x6 yz 8 , x2 y 2 z 9 = x10 , y 10 , z x10 , y 3 , z 8 x2 , y 9 , z 10 x4 , y 9 , z 6 ∩ ∩ ∩ ∩ x8 , y 10 , z 3 x9 , y 4 , z 8 x, y 10 , z 10 x6 , y 4 , z 9 ∩ ∩ ∩ ∩ x7 , y 8 , z 6 x5 , y 7 , z 9 x8 , y 8 , z 4 x10 , y 6 , z 2 ∩ ∩ ∩ ∩ x9 , y 5 , z 7 ∩ x7 , y 7 , z 7 ∩ x3 , y 9 , z 9 ∩ x10 , y, z 10 ∩ x9 , y 6 , z 4 ∩ x4 , y 10 , z 5 ∩ x6 , y 2 , z 10 3 12 9 11 10 7 8 6 2 5 1 4 Fig.