AAECC 1991: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes pp 333-339 | Cite as
Binary spherical geometric codes
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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
- [1]Conway, J. H. and Sloane, N. J. A. "Sphere packing, Lattices and Groups", Springer-Verlag, New-York, 1988.Google Scholar
- [2]Perret, M. "Multiplicative character sums and Kummer coverings", Acta Arithmetica, 59 no3 (1991), p. 75–86.Google Scholar
- [3]Perret, M. "Multiplicative character sums and non linear geometric codes", symposia of Eurocode 90, to appear in Lecture Notes in Computer Sciences, Springer.Google Scholar
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© Springer-Verlag Berlin Heidelberg 1991