By Peter Beelen, Diego Ruano (auth.), Maria Bras-Amorós, Tom Høholdt (eds.)

ISBN-10: 3642021808

ISBN-13: 9783642021800

ISBN-10: 3642021816

ISBN-13: 9783642021817

This publication constitutes the refereed complaints of the 18th overseas Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-18, held in Tarragona, Spain, in June 2009.

The 22 revised complete papers awarded including 7 prolonged absstracts have been rigorously reviewed and chosen from 50 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, variations, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.

**Read or Download Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 18th International Symposium, AAECC-18 2009, Tarragona, Spain, June 8-12, 2009. Proceedings PDF**

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**Additional info for Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 18th International Symposium, AAECC-18 2009, Tarragona, Spain, June 8-12, 2009. Proceedings**

**Example text**

U1 } ∪ {n ∈ N : n ≥ 2g} , H = 2H ¯ is a semigroup of genus γ and uγ < · · · < u1 ≤ 2g − 1 are precisely the where H γ odd nongaps of H up to 2g. Proof. 1. ¯ = Observe that H in the above Proposition has exactly γ even nongaps and H {h/2 : h ∈ H, h ≡ 0 (mod 2)}. The main result of this section is the following. 28 C. Munuera, F. Torres, and J. Villanueva Theorem 3. Let H be a sparse semigroup with g = 2g − (2γ + 1). If g ≥ 6γ + 4 ¯ ∪ {uγ , . . , u1 } ∪ {n ∈ N : n ≥ 2g}, where H ¯ is a semigroup of then H = 2H genus γ and ui = 2g − 2i + 1 for i = 1, .

H is Arf with g = 2g − 2; 2. H is sparse with g = 2g − 2; 3. g = 2 and H = {0, 3, 4, . }, or g = 3 and H = {0, 3, 5, 6, 7, . } = 3N0 ∪{h ∈ N : h ≥ 5}. Example 5. By using the above results we can compute all sparse semigroups with g = 2g − 4. First note that all these semigroups have genus g ≥ 4. Also g ≤ 7. If otherwise g ≥ 4k = 8, Theorem 2 implies g ≤ 11 − m and hence m = 2 or m = 3. In both cases 12 ∈ H. Since 7 = 10, we have 12 ≥ 2g which is a contradiction. Thus 4 ≤ g ≤ 7. Let g > 4. By Theorem 1(1) we have 2 ≤ m ≤ 4.

On numerical Semigroups and the Order Bound. J. Pure Appl. Algebra 212, 2271–2283 (2008) 11. : On the order bound of one-point algebraic geometry codes. J. Pure Appl. Algebra (to appear) 12. : Arf Numerical Semigroups. Journal of Algebra 276, 3–12 (2004) 13. : On γ-hyperelliptic numerical semigroups. Semigroup Forum 55, 364–379 (1997) 14. : Weierstrass points and double coverings of curves with applications: Symmetric numerical semigroups which cannot be realized as Weierstrass semigroups. Manuscripta Math.

### Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 18th International Symposium, AAECC-18 2009, Tarragona, Spain, June 8-12, 2009. Proceedings by Peter Beelen, Diego Ruano (auth.), Maria Bras-Amorós, Tom Høholdt (eds.)

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