Abstract
Let q be a power of an odd prime number and Fq be the finite field with q elements. We will construct a binary spherical code from an algebraic curve C defined over Fq and a rational divisor G on C, as the twist by the quadratic character η of the Goppa code L(G). The computation of the parameters of this code is based on the study of some character sums.
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Bibliography
Conway, J. H. and Sloane, N. J. A. "Sphere packing, Lattices and Groups", Springer-Verlag, New-York, 1988.
Perret, M. "Multiplicative character sums and Kummer coverings", Acta Arithmetica, 59 no3 (1991), p. 75–86.
Perret, M. "Multiplicative character sums and non linear geometric codes", symposia of Eurocode 90, to appear in Lecture Notes in Computer Sciences, Springer.
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© 1991 Springer-Verlag Berlin Heidelberg
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Perret, M. (1991). Binary spherical geometric codes. In: Mattson, H.F., Mora, T., Rao, T.R.N. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1991. Lecture Notes in Computer Science, vol 539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54522-0_121
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DOI: https://doi.org/10.1007/3-540-54522-0_121
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