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 ebook constitutes the refereed court cases 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 provided 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: earrings and fields, polynomials, diversifications, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.

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

**Sample text**

Furthermore, the generator matrices of RMs−1 (r − 1, m − 1) and RMs−1 (r, m − 1) can be obtained using Plotkin construction again from codes with m − 2 value.

Let H be a sparse semigroup of genus g with 2 g ≥ 3g then H is acute and o(H) = 2 g − g = 3g − 2K. g = 2g − K. If Proof. Notation as in equation (4). From Theorem 1, c0 = g +1, c1 = d1 = g −1 and c2 = d2 = g − 3. We have 2d1 + 1 = c0 + c1 − 1 = 2 g − 1 and thus H is acute. Now 2 g − 1 = ρ2 g −g and the proof follows from the above formula (∗) for o(H). Example 10. For g ≥ 7, let H = {0, g − 2, g, g + 3, g + 4 . } be the sparse semigroup of Example 1 (thus g = g + 2 = 2g − (g − 2)). It is easy to check that H is not near-acute.

6065, 13083-970, Campinas-SP, Brasil Abstract. We investigate the class of numerical semigroups verifying the property ρi+1 − ρi ≥ 2 for every two consecutive elements smaller than the conductor. These semigroups generalize Arf semigroups. 1 Introduction Let N0 be the set of nonnegative integers and H = {0 = ρ1 < ρ2 < · · ·} ⊆ N0 be a numerical semigroup of ﬁnite genus g. This means that the complement N0 \H is a set of g integers called gaps, Gaps(H) = { 1 , . . , g }. Then c = g + 1 is the smallest integer such that c + h ∈ H for all h ∈ N0 .

### 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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