Title :
Surfaces and the weight distribution of a family of codes
Author :
van der Vlugt, M.
Author_Institution :
Dept. of Math. & Comput. Sci., Leiden Univ., Netherlands
fDate :
7/1/1997 12:00:00 AM
Abstract :
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
Keywords :
algebraic geometric codes; binary sequences; cyclic codes; algebraic-geometric nature; binary trace codes; exponential sums; quadratic forms; theory of surfaces; trace map; weight distribution; Equations; Error correction codes; Galois fields; Geometry; H infinity control; Information theory; Upper bound;
Journal_Title :
Information Theory, IEEE Transactions on
