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Majority logic decoding using combinatorial designs (Corresp.)

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2 Author(s)

If the vectors of some constant weight in the dual of a binary linear code support a (\nu,b,r,k,\lambda ) balanced incomplete block design (BIBD), then it is possible to correct [(r + 2 - 1)/2\lambda ] errors with one-step majority logic decoding. This bound is generalized to the case when the vectors of certain constant weight in the dual code support a t -design. With the aid of this bound, the one-step majority logic decoding of the first, second, and third order Reed-Muller codes is examined.

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Information Theory, IEEE Transactions on  (Volume:21 ,  Issue: 5 )