Title :
A spectral characterization of correlation-immune combining functions
fDate :
5/1/1988 12:00:00 AM
Abstract :
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(ω) vanishes for all ω with Hamming weight between 1 and m, inclusive. This result is used to extend slightly Siegenthaler´s (IEEE Trans. Comput., vol. C-34, pp. 81-85, Jan. 1985) characterization of the algebraic normal form of correlation-immune combining functions
Keywords :
Boolean functions; Walsh functions; information theory; Boolean combining function; Hamming weight; Walsh transform; correlation-immune; spectral characterization; Binary sequences; Boolean functions; Galois fields; Hamming weight; Information processing; Information theory; Linear feedback shift registers; Mathematics; Random variables; Signal processing;
Journal_Title :
Information Theory, IEEE Transactions on
