| Parameters of Goppa codes revisited (2007) | |||||||||||||||
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| We discuss parameters of Goppa codes, such as minimum distance, covering radius, distance distribution, and generalized Hamming weights. By a variation on the exponential sums method and combinatorial arguments, we sharpen known bounds. 1 Preliminaries The interest in Goppa codes is no more to be proven. The study of their features highly rely on algebra and combinatorics. The main parameter studied before was minimum distance. Recently, others such as covering radius and generalized Hamming weights had got new impulse of interest. In this paper, we further explore parameters of Goppa codes and give new estimates. We improve on the conventional exponential sums method to sharpen the bounds on minimum distance and covering radius. Furthemore, bounds on absolute values of Krawtchouk polynomials allow us to get better estimates for the error term in the binomial approximation of the distance distribution of these codes. Finally, we use counting arguments to derive results on the second a... | |||||||||||||||
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