A350271 The covering radius of the first order Reed-Muller code RM(1,n).

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

Table of n, a(n) for n=1..8.

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. Yücel, 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

Adjacent sequences: A350268 A350269 A350270 * A350272 A350273 A350274

Keyword

nonn,hard,more

Author

Christof Beierle, Dec 22 2021

Status

approved