Saddle point techniques in asymptotic coding theory
D Gardy, P Solé - Workshop on Algebraic Coding, 1991 - Springer
D Gardy, P Solé
Workshop on Algebraic Coding, 1991•SpringerWe use asymptotic estimates on coefficients of generating functions to derive anew the
asymptotic behaviour of the volume of Hamming spheres and Lee spheres for small
alphabets. We then derive the asymptotic volume of Lee spheres for large alphabets, and an
asymptotic relation between the covering radius and the dual distance of binary codes.
asymptotic behaviour of the volume of Hamming spheres and Lee spheres for small
alphabets. We then derive the asymptotic volume of Lee spheres for large alphabets, and an
asymptotic relation between the covering radius and the dual distance of binary codes.
Abstract
We use asymptotic estimates on coefficients of generating functions to derive anew the asymptotic behaviour of the volume of Hamming spheres and Lee spheres for small alphabets. We then derive the asymptotic volume of Lee spheres for large alphabets, and an asymptotic relation between the covering radius and the dual distance of binary codes.
Springer
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