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Welch bounds : ウィキペディア英語版 | Welch bounds In mathematics, Welch bounds are a family of inequalities pertinent to the problem of evenly spreading a set of unit vectors in a vector space. The bounds are important tools in the design and analysis of certain methods in telecommunication engineering, particularly in coding theory. The bounds were originally published in a 1974 paper by L. R. Welch. ==Mathematical statement==
If are unit vectors in , define , where is the usual inner product on . Then the following inequalities hold for : :
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