On the Covering Radii of Binary RM Codes in the Set of Resilient Boolean Functions

On the Covering Radii of Binary RM Codes in the Set of Resilient Boolean Functions

Let R-t,R-n be the set of t-resilient Boolean functions in n variables, and let (p) over cap (t, r, n) be the maximum distance between t-resilient functions and the rth-order Reed-Muller code RM (r, n). We prove that,6(t, 2, 6) = 16 for t = 0, 1, 2 and)5(3, 2, 7) = 32, from which we derive the lower...

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Veröffentlicht in:IEEE Transactions on Information Theory 2005, Vol.51 (3), p.1182-1189
Hauptverfasser: Borissov, Y, Braeken, An, Nikova, Svetla, Preneel, Bart
Format: Artikel
Sprache:eng
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Zusammenfassung:Let R-t,R-n be the set of t-resilient Boolean functions in n variables, and let (p) over cap (t, r, n) be the maximum distance between t-resilient functions and the rth-order Reed-Muller code RM (r, n). We prove that,6(t, 2, 6) = 16 for t = 0, 1, 2 and)5(3, 2, 7) = 32, from which we derive the lower bound (p) over cap (t, 2, n) greater than or equal to 2(n-2) with t less than or equal to n - 4.
ISSN:0018-9448