Abstract
If the vectors of some constant weight in the dual of a binary linear code support a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(\nu,b,r,k,\lambda)</tex> balanced incomplete block design (BIBD), then it is possible to correct <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[(r + 2 - 1)/2\lambda]</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</tex> -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.
Published Version
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