Paper 2011/571
Lower Bound on Covering Radius of Reed-Muller Codes in Set of Balanced Functions
Brajesh Kumar Singh and Sugata Gangopadhyay
Abstract
In this paper, we derive a general lower bound on covering radius, $\hat{\rho}(0, 2, n)$ of Reed-Muller code $RM(2, n)$ in $R_{0, n}$, set of balanced Boolean functions on $n$ variables where $n = 2t + 1$, $t$ is an odd prime satisfying one of the following conditions \begin{enumerate} \item[(i)] $ord_t(2) = t - 1$; \item[(ii)] $t=2s + 1$, $s$ is odd, and $ord_t(2) = s$. \end{enumerate} Further, it is proved that $\hat{\rho}(0, 2, 11) \geq 806$, which is improved upon the bound obtained by Kurosawa et al.'s bound ({\em IEEE Trans. Inform. Theory}, vol. 50, no. 3, pp. 468-475, 2004).
Metadata
- Available format(s)
- -- withdrawn --
- Category
- Foundations
- Publication info
- Published elsewhere. Not submitted any where yet.
- Contact author(s)
- gsugata @ gmail com
- History
- 2011-12-01: withdrawn
- 2011-10-25: received
- See all versions
- Short URL
- https://ia.cr/2011/571
- License
-
CC BY