By Edgar Martinez-Moro, Carlos Munuera, Diego Ruano

"Advances in Algebraic Geometry Codes" provides the main profitable functions of algebraic geometry to the sphere of error-correcting codes, that are utilized in the whilst one sends info via a loud channel. The noise in a channel is the corruption of part of the knowledge as a result of both interferences within the telecommunications or degradation of the information-storing help (for example, compact disc). An error-correcting code therefore provides additional info to the message to be transmitted with the purpose of getting better the despatched details. With contributions shape popular researchers, this pioneering booklet may be of worth to mathematicians, computing device scientists, and engineers in details thought.

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**Extra resources for Advances In Algebraic Geometry Codes**

**Example text**

Fg ∈ L(G − Q1 · · · − Qt ) be functions with increasing orders of vanishing at P0 in the range {0, . . , 2g}. And let h0 , . . , hg ∈ L(2gP0 ) be functions with increasing pole order at P0 in the range {0, . . , 2g}. By the pigeonhole principle there exist fi and gj such that fi gj is a unit at P0 . 14, let f0 , f1 , . . , fg+t ∈ L(G) be functions with increasing orders of vanishing at P0 in the range {0, . . , 2g+t}. And let g0 , . . , gg+t ∈ L((2g+t)P0 ) be functions with increasing pole order at P0 in the range {0, .

8 Literature . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Introduction The work on decoding of algebraic geometry codes started in 1986 and in the following 10 years a lot of papers appeared. The paper [11] surveys all the work on decoding until 1995. In this chapter we will present decoding algorithms using recent ideas and methods.

Shum, I. Aleshnikov, P. V. Kumar, H. Stichtenoth, and V. Deolaikar, A low-complexity algorithm for the construction of algebraic-geometric codes better than the Gilbert-Varshamov bound, IEEE Trans. Inform. Theory. 47 (6), 2225–2241, (2001). S. A. Stepanov, Codes on algebraic curves. (Kluwer Academic/Plenum Publishers, New York, 1999). H. Stichtenoth, Algebraic function fields and codes. Universitext, (SpringerVerlag, Berlin, 1993). H. Stichtenoth and C. Xing, Excellent nonlinear codes from algebraic function fields, IEEE Trans.