Abstract
Using recent results from complexity theory, we show that, under the assumption P≠NP, no polynomial time algorithm can compute an upper bound for the number of error locations of a word y with respect to a code C, which is guaranteed to be within a constant ratio of the true (Hamming) distance of y to C.
Thus the barrier which prevents the design of very general decoding algorithms that would apply to unstructured codes is even more solid than was thought before.
We also give an analogous result for integer lattices.
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© 1993 Springer-Verlag Berlin Heidelberg
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Stern, J. (1993). Approximating the number of error locations within a constant ratio is NP-complete. In: Cohen, G., Mora, T., Moreno, O. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1993. Lecture Notes in Computer Science, vol 673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56686-4_54
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DOI: https://doi.org/10.1007/3-540-56686-4_54
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