July 15, 2017

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

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

This e-book constitutes the refereed lawsuits 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 provided 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: earrings and fields, polynomials, variations, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.

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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 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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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. Corollary 2). Sparse Numerical Semigroups 5 29 On the Order of Semigroups In this section we are interested in the order bound of sparse semigroups.

IEEE Trans. Inform. Theory 46(7), 2634–2638 (2000) 6. : Algebraic Geometry codes. , Huffman, C. ) Handbook of Coding Theory, pp. 871–961. Elsevier, Amsterdam (1998) 7. : Stable ideal and Arf semigroups. Amer. J. Math. 97, 791–813 (1975) 8. : A note on the order bound on the minimum distance of AG codes and acute semigroups. Advances in Mathematics of Communications 2(2), 175–181 (2008) 9. : Weierstrass semigroups and the canonical ideal of non-trigonal curves. Manuscripta Math. 71, 431–450 (1991) 10.

We will prove that these codes are equal. This proposition will be used for the classification of some of the RMs (r, m) codes in Section 4, and it will also be used to calculate the rank of these codes as exceptions. Proposition 7. Given two codes RMs (r, m) and RMs−1 (r, m) of type 2γ 4δ and 2γ 4δ , respectively, such that m ≥ 3 is odd, r ≥ 2 is even, and s = m−1 2 , then RMs (r, m) = RMs−1 (r, m). Rank for Some Families of Quaternary Reed-Muller Codes 49 Proof. The generator matrix Gs−1(r,m) of RMs−1 (r, m) is obtained using the Plotkin construction from RMs−1 (r − 1, m − 1) and RMs−1 (r, m − 1).

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