An in nite class of counterexamples to a conjecture concerning non-linear resilient functions
نویسنده
چکیده
The main construction for resilient functions uses linear error-correcting codes; a resilient function constructed in this way is said to be linear. It has been conjectured that if there exists a resilient function, then there exists a linear function with the same parameters. In this note, we construct innnite classes of non-linear resilient functions from the Kerdock and Preparata codes. We also show that there do not exist linear resilient functions having the same parameters as the functions that we construct from the Kerdock codes. Thus, the aforementioned conjecture is disproved.
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