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By Elwyn R. Berlekamp

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Extra info for A Survey of Algebraic Coding Theory: Lectures Held at the Department of Automation and Information, July 1970

Example text

BC H - 1), n- Cd 8 c. H - that for all ~) , ••• , n - 1 i, E. $. H . We then replace i. BCH Bound by ~- 53 b to obtain ()C, et n £ Lf. { 0, 1,2,, ... H. acH values of f ~ c coc. i. - b) X l, . D. A change of primitive root multiplies the set K by some number J which is relatively prime to r1, and this multiplication will effect the size of the gaps inK. Since the distance structure of the code cannot depend on the choice of primitive root, it follows that the distance of the code is larger than any consecutive gap which occurs in choice of J JK for any relatively prime ton.

From a practical point of view, threshold decoding is most attractive when r is small. For moderate values of r the number of intermediate subspaces whose parity checks must be computed can be very large. IZ . If d. and N are large, then most error patterns of weight slightly more than d/2 will not be evenly distributed among the translates of any r-dimensional subspace S. zm- '"- 1 Less than half of these translates will contain an odd number of errors and the elections will determine the correct values of Q(S)Et for all r-dimensional subspaces S.

H - that for all ~) , ••• , n - 1 i, E. $. H . We then replace i. BCH Bound by ~- 53 b to obtain ()C, et n £ Lf. { 0, 1,2,, ... H. acH values of f ~ c coc. i. - b) X l, . D. A change of primitive root multiplies the set K by some number J which is relatively prime to r1, and this multiplication will effect the size of the gaps inK. Since the distance structure of the code cannot depend on the choice of primitive root, it follows that the distance of the code is larger than any consecutive gap which occurs in choice of J JK for any relatively prime ton.

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