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Books > Science & Mathematics > Mathematics > Algebra
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Codes on Algebraic Curves (Hardcover, 1999 ed.)
Loot Price: R3,810
Discovery Miles 38 100
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Codes on Algebraic Curves (Hardcover, 1999 ed.)
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This is a self-contained introduction to algebraic curves over
finite fields and geometric Goppa codes. There are four main
divisions in the book. The first is a brief exposition of basic
concepts and facts of the theory of error-correcting codes (Part
I). The second is a complete presentation of the theory of
algebraic curves, especially the curves defined over finite fields
(Part II). The third is a detailed description of the theory of
classical modular curves and their reduction modulo a prime number
(Part III). The fourth (and basic) is the construction of geometric
Goppa codes and the production of asymptotically good linear codes
coming from algebraic curves over finite fields (Part IV). The
theory of geometric Goppa codes is a fascinating topic where two
extremes meet: the highly abstract and deep theory of algebraic
(specifically modular) curves over finite fields and the very
concrete problems in the engineering of information transmission.
At the present time there are two essentially different ways to
produce asymptotically good codes coming from algebraic curves over
a finite field with an extremely large number of rational points.
The first way, developed by M. A. Tsfasman, S. G. Vladut and Th.
Zink [210], is rather difficult and assumes a serious acquaintance
with the theory of modular curves and their reduction modulo a
prime number. The second way, proposed recently by A.
General
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