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Fast decoding of codes from algebraic plane curves

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4 Author(s)
J. Justesen ; Tech. Univ. of Denmark, Lyngby, Denmark ; K. J. Larsen ; H. E. Jensen ; T. Hoholdt

Improvement to an earlier decoding algorithm for codes from algebraic geometry is presented. For codes from an arbitrary regular plane curve the authors correct up to d*/2-m2 /8+m/4-9/8 errors, where d* is the designed distance of the code and m is the degree of the curve. The complexity of finding the error locator is O(n7/3 ), where n is the length of the code. For codes from Hermitian curves the complexity of finding the error values, given the error locator, is O(n2), and the same complexity can be obtained in the general case if only d*/2-m2/2 errors are corrected

Published in:

IEEE Transactions on Information Theory  (Volume:38 ,  Issue: 1 )