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Surfaces and the weight distribution of a family of codes

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1 Author(s)
van der Vlugt, M. ; Dept. of Math. & Comput. Sci., Leiden Univ., Netherlands

We derive the weight distribution of the binary trace codes with words (Tr(axq+1+bx3+cx))x∈F*(q2) where a, b, c∈F(q2) and Tr is the trace map from F(q2) to F2. The weights of these words determine the exponential sums which were considered earlier by Moreno and Kumar (1994) and Lahtonen (1995). Results from the theory of quadratic forms play a role but the decisive argument is of an algebraic-geometric nature, namely, from the theory of surfaces

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Information Theory, IEEE Transactions on  (Volume:43 ,  Issue: 4 )