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Exponential sums and Goppa codes. II

机译:指数模拟人生和伟大的守则。电子工程

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For pt.I, see Proc. AMS, vol.III, p.523-31 (1991). The minimum distance of a Goppa code is found when the length of code satisfies a certain inequality on the degree of the Goppa polynomial. In order to do this, conditions are improved on a theorem of E. Bombieri (1966). This improvement is used also to generalize a previous result on the minimum distance of the dual of a Goppa code. This approach is generalized and results are obtained about the parameters of a class of subfield subcodes of geometric Goppa codes; in other words, the covering radii are estimated, and further, the number of information symbols whenever the minimum distance is small in relation to the length of the code is found. Finally, a bound on the minimum distance of the dual code is discussed.
机译:关于pt.I,请参见Proc。 AMS,第3卷,第523-31页(1991)。当代码的长度满足Goppa多项式的阶数的某个不等式时,便可以找到Goppa代码的最小距离。为此,在E. Bombieri(1966)的一个定理上改进了条件。该改进还用于概括关于Goppa码对偶的最小距离的先前结果。对该方法进行了概括,得到了关于几何Goppa码的一类子场子码的参数的结果。换句话说,估计覆盖半径,并且,每当相对于代码长度的最小距离小时,信息符号的数量就被找到。最后,讨论了对偶代码最小距离的界限。

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