Applied Algebra, Algebraic Algorithms and Error-Correcting by Peter Beelen, Diego Ruano (auth.), Maria Bras-Amorós, Tom

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

This ebook constitutes the refereed complaints of the 18th foreign 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 conscientiously reviewed and chosen from 50 submissions. one of the topics addressed are block codes, together with list-decoding algorithms; algebra and codes: jewelry, fields, algebraic geometry codes; algebra: jewelry and fields, polynomials, diversifications, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.

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

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A new quaternary linear code PC(A, B) is defined as PC(A, B) = {(u|u + v) : u ∈ A, v ∈ B}. It is easy to see that if GA and GB are generator matrices of A and B, respectively, then the matrix GA GA GP C = 0 GB is a generator matrix of the code PC(A, B). Moreover, the code PC(A, B) is of length 2n, type 2γA +γB 4δA +δB , and minimum distance d = min{2dA , dB } [14],[15]. Definition 3 (BQ-Plotkin Construction). Let A, B, and C be three quaternary linear codes of length n; types 2γA 4δA , 2γB 4δB , and 2γC 4δC ; and minimum distances dA , dB , and dC , respectively.

Munuera1 , F. Torres2 , and J. Villanueva2 1 2 Dept. P. 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 , .

N ∈ N0 : n ≥ 2g − 1}. Example 8. Let H be a semigroup of genus g ≥ 16 with following statements are equivalent: g = 2g − 5. The 1. H is Arf; 2. H is sparse; ¯ ∪ {2g − 3, 2g − 1}, where H ¯ is 3. H is ordinary 2-hyperelliptic, that is H = 2H a semigroup of genus 2. ¯ of genus γ which are not Example 9. For every γ ≥ 3, there exist semigroups H Arf. For example, H := N0 \ {1, 2, . . , γ − 1, γ + 2}. Thus for every γ ≥ 3 there exist ordinary γ-hyperelliptic semigroups having largest gap g odd, which are not Arf property (cf.

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