Generalized Bezout's theorem and its applications in coding theory
- 1 January 1997
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 43 (6) , 1799-1810
- https://doi.org/10.1109/18.641546
Abstract
This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more plane curves. A new approach to determine a lower bound on the minimum distance for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d=4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d⩾5, these new codes are better than the known AG codes defined from whole spaces. The Klein codes [22, 16, 5] and [22, 15, 6] over GF(23), and the improved Hermitian code [64, 56, 6] over GF(24) are also constructedKeywords
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