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 provided including six invited survey papers have been rigorously 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, interpreting tools, code development, algebraic curves, cryptography, codes and interpreting, convolutional codes, designs, deciphering 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**

The familiar duality of planar graphs now becomes Alexander duality for monomial ideals as deﬁned by Miller [15], and yields an eﬃcient algorithm for problem (iii). However, it is more diﬃcult to construct cellular resolutions which are minimal. There seems to be no n-dimensional analogue to Theorem 3. One obstruction is that the minimal resolution may depend on the characteristic of the ﬁeld K. Any general formula for minimal resolutions is expected to involve homological algebra over the lcm-lattice of Gasharov, Peeva and Welker [12].

In particular, CGL has dimension [G : H] · dim L. The left CG-module CGL is said to be induced by L. A look at the corresponding matrix representations leads to the following deﬁnition. Let H be a subgroup of the group G, T := (g1 , . . , gr ) a transversal of the left cosets of H in G and let F be a representation of CH of degree f. The induced representation F ↑T G of CG of degree f · r is deﬁned for x ∈ G by F ↑T G(x) := (F˙ (gi−1 xgj ))1≤i,j≤r ∈ (Cf ×f )r×r , where F˙ (y) := F (y) if y ∈ H, and F˙ (y) is the f-square all zero matrix, if y ∈ G \ H.

10) that with q restricted to the given subsequence, lim γq ≤ q→∞ 1 − δ∗ H(0) = 0, δ∗ which contradicts Theorem 22. On the other hand, if δ ∗ = 0, we have from Corollary 35 that for q large enough u(q, δ(q)) < δ(q)2 . 10) again, for large enough q, we have γq ≤ (1 − δ(q)) H(δ(q)2 ) . δ(q) But since H(x2 )/x → 0 as x → 0, with q restricted to the given subsequence, H(δ(q)2 ) = 0, q→∞ δ(q) lim γq ≤ lim q→∞ again contradicting Theorem 22. 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.

### 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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