The Covering Radius of the Reed–Muller Code <i>RM</i>(<i>m</i> – 4, <i>m</i>) in <i>RM</i>(<i>m</i> – 3, <i>m</i>)

We present methods for computing the distance from a Boolean polynomial on $m$ variables of degree notation="LaTeX">$m-3$ (i.e., member Reed–Muller code notation="LaTeX">$RM(m-3, m)$ ) to space lower-degree polynomials ( notation="LaTeX">$RM(m-4, ). The give verifiable certificates both lower and upper bounds this distance. By applying these representative lists polynomials, we show that covering radius notation="LaTeX">$RM(4,8)$ in notation="LaTeX">$RM(5,8)$ is 26 notation="LaTeX">$RM(5,9)$ notation="LaTeX">$RM(6,9)$ between 28 32 inclusive, get improved higher . also apply our various literature, thereby improving known 2-resilient