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 publication 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 offered 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, earrings and fields, deciphering tools, code development, algebraic curves, cryptography, codes and deciphering, convolutional codes, designs, deciphering of block codes, modulation and codes, Gröbner bases and AG codes, and polynomials.

**Read Online 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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**Additional 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**

We claim that the following converse to Theorem 3 holds. Theorem 4. For every 3-connected planar graph G there exists a monomial ideal M in 3 variables which is minimally resolved by the bounded regions of G. 1] which states that 3-connected planar graphs are the edge graphs of 3-dimensional convex polytopes. 1, pp. 128], as explained in [3, §6]. The general non-triangulated case is more diﬃcult. 1]. The complete proof of Theorem 4 is “under construction” and will be published elsewhere. In Figure 4 is a non-trivial example illustrating the encoding of a planar graph G by a monomial ideal M.

For every 3-connected planar graph G there exists a monomial ideal M in 3 variables which is minimally resolved by the bounded regions of G. 1] which states that 3-connected planar graphs are the edge graphs of 3-dimensional convex polytopes. 1, pp. 128], as explained in [3, §6]. The general non-triangulated case is more diﬃcult. 1]. The complete proof of Theorem 4 is “under construction” and will be published elsewhere. In Figure 4 is a non-trivial example illustrating the encoding of a planar graph G by a monomial ideal M.

18 Hui Jin and Robert J. McEliece We have therefore shown that the only possible accumulation point of the set {δ(q)} is 1/2, which proves that the limit of the δ(q)’s exists and equals 1/2. ✷ We can now prove the main theorem: Proof of Theorem 21. We have, for every q, γq = qc0 (q) = q 1 − δ(q) 1 − e−2rq (δ(q)) . 9), we obtain γq ≤ q 1 − δ(q) rq (δ(q)). δ(q) Now from Corollary 32, we know that rq (δ) ≤ (log 2)/q, so that we have γq ≤ 1 − δ(q) log 2. δ(q) But by Proposition 31, limq→∞ δ(q) = 1/2, so lim sup γq ≤ log 2.

### 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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