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Can anyone give an example of 7 binary covering numbers that cover all 32 possible 5 digit binary numbers with an error of up to 1 place? I have proved that 6 binary numbers do not exist, but I am having trouble finding 7 that do. I have combed the interweaves but to no avail. Thank you so much!

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    I think what you're asking for is a set of 7 5-bit numbers such that every 5-bit number agrees with at least one of your 7 numbers in at least 4 of its bits. Is that a correct understanding of your question?2012-02-09
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    Yes that is correct. And I have already proven there does not exist a set of 6 such numbers.2012-02-09

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