Guo-Zhen Xiao

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It is shown that a Boolean combining function f(x) of n variables is mth-order correlation immune if and only if its Walsh transform F(w) vanishes for all w with Hamming weights between 1 and m, inclusive. This result is used to extend slightly Siegenthaler’s characterization of the algebraic normal form of correlation-immune combining functions.
The probability of undetected error P,(E) for the primitive<lb>triple-error-correcting BCH codes of blocklength 2m 1 used solely for<lb>error detection on a binary symmetric channel with cross-over probabil-<lb>ity E 5 1/2 is examined. It is shown that for odd values of m , P,(E)<lb>increases monotonically with E. For even values of m, this is(More)
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