GENERALIZED BEZOUT THEOREM AND ITS APPLICATIONS IN CODING THEORY

This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of in tersection of two or more plane curves. A new approach to determine a lower bound on the minimum distance for algebraic-geometric codes defi ned from a class of plane curves is introduced, based on the generaliz ed Bezout theorem. Examples of more efficient linear codes are constru cted using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better t han or equal to the known linear codes. For d greater than or equal to 5, these new codes are better than the known AG codes defined from wh ole spaces. The Klein codes [22, 16, 5] and [22, 15, 6] over GF (2(3)) , and the improved Hermitian code [64, 56, 6] over GF(2(4)) are also c onstructed.