Titlebook: Algebraic-Geometric Codes; M. A. Tsfasman,S. G. Vlăduţ Book 1991 Kluwer Academic Publishers and Copyright Holders 1991 algebraic curve.ana

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interlude

Democracy Deferred: Lessons for the Future,The general discussion of the previous chapter leaves us a bit in the air without examples of AG-codes for which it is possible to calculate the parameters and to compare them with codes obtained by non-algebraic-geometric constructions.

BOGUS

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Examples and ConstructionsIn this chapter we present several examples of codes. Each example is in fact a method to construct some family of codes, which (in some way or other) have rather good parameters. Since in many cases these families are predecessors of algebraic-geometric codes, we try to choose constructions that are easy to generalize in that direction.

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千篇一律

Constructions and PropertiesThese exist several essentially equivalent ways to construct linear codes starting from algebraic curves (and also from varieties of higher dimensions). For curves, the codes we get can be rather well described: we can bound their parameters and weight spectra, we understand the duality.

同步左右

Endoscope

翻布寻找

Is Democracy the Best Form of Government?,rgation bound. For small . this bound coincides with the Gilbert-Varshamov bound, and if . is large enough, it is a bit better than the maximum of the Gilbert-Varshamov bound and the basic AG-bound, smoothing the angles at points of their intersection. The basic AG-bound is constructive, applying to

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Asymptotic Problems - just as our problem of finding out the best possible parameters of a code - passing to the limit for . → ∞ helps us to avoid “deviations” and to understand the behaviour of parameters better. In this chapter we state the problems rigorously and discuss those results that do not use algebraic-geom