**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).

**Category / Keywords: **foundations /

**Publication Info: **Not submitted any where yet.

**Date: **received 21 Oct 2011, withdrawn 1 Dec 2011

**Contact author: **gsugata at gmail com

**Available format(s): **(-- withdrawn --)

**Version: **20111201:114715 (All versions of this report)

**Short URL: **ia.cr/2011/571

**Discussion forum: **Show discussion | Start new discussion

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