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A350271
The covering radius of the first order Reed-Muller code RM(1,n).
0
0, 1, 2, 6, 12, 28, 56, 120
OFFSET
1,3
COMMENTS
242 <= a(9) <= 244.
For odd values of n, we have 2^(n-1) - 2^((n-1)/2) <= a(n) <= 2*floor(2^(n-2) - 2^(n/2-2)).
LINKS
C. Carlet, Boolean Functions for Cryptography and Coding Theory, Cambridge University Press (2021), Section 4.1.6.
T. Helleseth, T. Klove and J. Mykkeltveit, On the covering radius of binary codes (Corresp.), IEEE Transactions on Information Theory, Vol. 24 (1978).
X. Hou, On the norm and covering radius of the first-order Reed-Muller codes, IEEE Transactions on Information Theory, Vol. 43 (1997).
S. Kavut and M. D. YĆ¼cel, 9-variable Boolean functions with nonlinearity 242 in the generalized rotation symmetric class, Information and Computation, Vol. 208 (2010).
O. S. Rothaus, On "bent" functions, Journal of Combinatorial Theory, Series A, Vol. 20 (1976).
FORMULA
a(2n) = A006516(n).
CROSSREFS
Cf. A006516.
Sequence in context: A112510 A284449 A011949 * A089820 A122746 A191394
KEYWORD
nonn,hard,more
AUTHOR
Christof Beierle, Dec 22 2021
STATUS
approved