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

By Edgar Martinez-Moro, Carlos Munuera, Diego Ruano

"Advances in Algebraic Geometry Codes" offers the main winning purposes of algebraic geometry to the sector of error-correcting codes, that are utilized in the whilst one sends details via a loud channel. The noise in a channel is the corruption of part of the knowledge because of both interferences within the telecommunications or degradation of the information-storing help (for example, compact disc). An error-correcting code hence provides additional details to the message to be transmitted with the purpose of convalescing the despatched details. With contributions shape popular researchers, this pioneering ebook can be of price to mathematicians, machine scientists, and engineers in details concept.

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Deligne-Lusztig curves X/Fq . Type Unitary Suzuki Ree X y r + y = xr+1 . y q + y = xq0 (xq + x). q g N q = r2 r(r − 1)/2 r3 + 1 q = 2q02 ≥ 8. q0 (q − 1) q2 + 1 y q − y = xq0 (xq − x), z q − z = xq0 (y q − y). q = 3q02 ≥ 27. 3 q (q − 1)(q + q0 + 1) 0 2 q3 + 1 conductor r+2 2q0 + 2 3q0 + 3 Serre initiated the construction of curves with many points using class field theory. This has been a very successful method to show that certain pairs (N, g) occur as the number of rational points and the genus of a curve.

Sn ) be a vector that differs in no more than t positions from the vector (f (P1 ), . . , f (Pn )). Among the values for f (P0 ) that are returned by the reconstruction procedure when it is applied with F = tP0 , . . , (t + 2g)P0 , the correct value for f (P0 ) outnumbers any other value. algebraic August 25, 2008 10:59 World Scientific Review Volume - 9in x 6in Algebraic Geometry Codes: General Theory algebraic 41 Proof. dim L((t + 2g)P0 − Q) − dim L(tP0 − Q − P0 ) = g + 1. For F = tP0 , .

Theory. 43(1), 128–135, (1997). J. L. Walker, Codes and curves. vol. 7, Student Mathematical Library, (American Mathematical Society, Providence, RI, 2000). IAS/Park City Mathematical Subseries. K. Yang and P. V. Kumar. On the true minimum distance of Hermitian codes. In Coding theory and algebraic geometry (Luminy, 1991), vol. , pp. 99–107. Springer, Berlin, (1992). C. Xing, Nonlinear codes from algebraic curves improving the TsfasmanVl˘ adut¸-Zink bound, IEEE Trans. Inform. Theory. 49(7), 1653–1657, (2003).

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