# 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 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 awarded including 7 prolonged absstracts have been rigorously reviewed and chosen from 50 submissions. one of the topics addressed are block codes, together with list-decoding algorithms; algebra and codes: earrings, 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.

**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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1(1), 67–77 (1990) 13. : Algebraic geometry of codes. In: Handbook of coding theory, vol. I, II, pp. 871–961. North-Holland, Amsterdam (1998) 14. : On the index of the Weierstrass semigroup of a pair of points on a curve. Arch. Math. (Basel) 62(1), 73–82 (1994) 15. : The minimum distance of codes in an array coming from telescopic semigroups. IEEE Trans. Inform. Theory 41(6, part 1), 1720–1732 (1995); Special issue on algebraic geometry codes 16. : A generalized ﬂoor bound for the minimum distance of geometric Goppa codes.

185. Springer, New York (2005) 3. : On the equivalence between Berlekamp’s and Euclid’s algorithms. IEEE Trans. Inform. Theory 33(3), 428–431 (1987) 4. : On decoding BCH codes. IEEE Trans. Information Theory IT11, 549–557 (1965) 5. : On the equivalence of the Berlekamp-Massey and the Euclidean algorithms for decoding. IEEE Trans. Inform. Theory 46(7), 2614– 2624 (2000) 6. : Shift-register synthesis and BCH decoding. IEEE Trans. Information Theory IT-15, 122–127 (1969) 42 M. E. O’Sullivan 7. : The Key Equation for One-Point Codes, ch.

G. In particular m ≤ K. 2. If i = 2i − K then j = 2j − K for j = i, . . , g. 3. If g ≥ 2K − 1 then i = 2i − K for all i = 2K − 2, . . , g. Proof. (1) By the sparse property, g − i ≤ 2(g − i) so that i ≥ 2i − K. Then 2(j + 1) − K ≤ j+1 ≤ j + 2 and the result follows. (2) is clear. (3) Since g = 2g − K by deﬁnition of K, it is enough to prove that i+1 = i + 2 for i = 2k − 2, . . , g − 1. We use induction on j = g − i and thus we have to prove the statement g−j = g−j+1 − 2 for j = 1, . . , g − 2K + 2.