Read e-book online Advances In Algebraic Geometry Codes PDF

By Edgar Martinez-Moro, Carlos Munuera, Diego Ruano

ISBN-10: 981279400X

ISBN-13: 9789812794000

"Advances in Algebraic Geometry Codes" provides the main winning functions of algebraic geometry to the sphere of error-correcting codes, that are utilized in the while one sends details via a loud channel. The noise in a channel is the corruption of part of the data as a result of both interferences within the telecommunications or degradation of the information-storing aid (for example, compact disc). An error-correcting code hence provides additional details to the message to be transmitted with the purpose of improving the despatched details. With contributions shape well known researchers, this pioneering e-book may be of worth to mathematicians, desktop scientists, and engineers in details concept.

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58] H. Maharaj and G. L. Matthews, On the floor and the ceiling of a divisor, Finite Fields Appl. 12(1), 38–55, (2006). [59] H. Maharaj. Explicit towers and codes. In Recent trends in coding theory and its applications, vol. 41, AMS/IP Stud. Adv. , pp. 35–71. Amer. Math. , Providence, RI, (2007). [60] G. L. Matthews, Weierstrass pairs and minimum distance of Goppa codes, Des. Codes Cryptogr. 22(2), 107–121, (2001). [61] G. L. Matthews, Codes from the Suzuki function field, IEEE Trans. Inform. Theory.

Secret reconstruction for algebraic-geometric LSSSs An ideal F-linear secret sharing scheme Σ = Σ0 (Π) on the set of players {1, 2, . . , n} is defined as an F-linear map Π : E −→ Fn+1 . For x ∈ E, the values π1 (x), . . , πn (x) ∈ F are the shares of the secret value π0 (x) ∈ F. We recast the main properties of a linear secret sharing scheme in the language of geometric Goppa codes. We also show that every geometric Goppa code can be decoded up to half the designed distance. M. Duursma Let X /F be a curve.

Technische Universiteit Eindhoven, Eindhoven, 1993). Dissertation, Technische Universiteit Eindhoven, Eindhoven, 1993. I. M. Duursma and R. K¨ otter, Error-locating pairs for cyclic codes, IEEE Trans. Inform. Theory. 40(4), 1108–1121, (1994). I. M. Duursma, Monomial embeddings of the Klein curve, Discrete Math. 208/209, 235–246, (1999). Combinatorics (Assisi, 1996). I. M. Duursma, Weight distributions of geometric Goppa codes, Trans. Amer. Math. Soc. 351(9), 3609–3639, (1999). I. M. Duursma, C.

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Advances In Algebraic Geometry Codes by Edgar Martinez-Moro, Carlos Munuera, Diego Ruano


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