Connection With Epsilon-balanced Error-correcting Codes
There is a close connection between -biased sets and -balanced linear error-correcting codes. A linear code of message length and block length is -balanced if the Hamming weight of every nonzero codeword is between and . Since is a linear code, its generator matrix is an -matrix over with .
Then it holds that a multiset is -biased if and only if the linear code, whose columns are exactly elements of, is -balanced.
Read more about this topic: Epsilon-Biased Sample Spaces
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