A spectral characterization of correlation-immune combining functions
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( omega ) vanishes for all omega with Hamming weight between 1 and m, inclusive. This result is used to extend slightly Siegenthaler's (IEEE Trans. Comput., vol....
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| Veröffentlicht in: | IEEE transactions on information theory 1988-05, Vol.34 (3), p.569-571 |
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| container_title | IEEE transactions on information theory |
| container_volume | 34 |
| creator | Xiao, G.-Z. Massey, J.L. |
| description | 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( omega ) vanishes for all omega 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.< > |
| doi_str_mv | 10.1109/18.6037 |
| format | Article |
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| ispartof | IEEE transactions on information theory, 1988-05, Vol.34 (3), p.569-571 |
| issn | 0018-9448 1557-9654 |
| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Binary sequences Boolean functions Cryptography Exact sciences and technology Galois fields Hamming weight Information processing Information theory Information, signal and communications theory Linear feedback shift registers Mathematics Random variables Signal and communications theory Signal processing Telecommunications and information theory |
| title | A spectral characterization of correlation-immune combining functions |
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