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

0, 1, 2, 6, 12, 28, 56, 120

Offset: 1

Author

Christof Beierle, Dec 22 2021

Keywords

• nonn
• hard
• more

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. 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).

Crossrefs

Cf. A006516.

Formula

a(2n) = A006516(n).