Abstract
A linear code of block length n possessing minimum weight d has one code word of weight zero, and no other code words of weight less than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> . The weight distribution of the code is given by the set of all <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W(j), d \leq j \leq n</tex> , describing the number of code words having a weight of exactly <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</tex> . Exact weight distributions are known for only a handful of linear codes. This paper presents an explicit upper bound upon <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W(j)</tex> as a function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, d</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</tex> . The bound has general applicability to all linear codes.
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