From 8270b01aabc26ad5f3cbf05a11d75d9a49fc7789 Mon Sep 17 00:00:00 2001 From: Aaron Huber Date: Thu, 25 Jul 2019 09:59:33 -0400 Subject: [PATCH] Working on generalizing v_t --- hash_const.tex | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/hash_const.tex b/hash_const.tex index 5a2b023..16ab97f 100644 --- a/hash_const.tex +++ b/hash_const.tex @@ -65,7 +65,9 @@ Using the same argument as in $\gIJ$ yields \end{equation*} Setting $T_3 = \sum\limits_{\wVec \in \pw \st \sketchPolarParam{\wVec} = 0}\kMapParam{\wVec}$, $T_4 = \sum\limits_{\wVec \in \pw \st \sketchPolarParam{\wVec} = 1}\kMapParam{\wVec}$ gives an exact calculation for each term given a fixed $\buck$: \begin{equation*} -T_3 = \gVt{(k \cdot)} | \{\wVec \st \matrixH \cdot \wVec = \buck^{(0)}, \kMapParam{\wVec} = \gVt{(k) }1\}\rightarrow T_3 \in [0, 2^{\numTup - rank(\matrixH')}] +T_3 = \gVt{\sum_{\substack{k \in \{\wVec \st \\ + \matrixH \cdot \wVec = \buck^{(0)},\\ + \kMapParam{\wVec} = k\}}}k} | \{\wVec \st \matrixH \cdot \wVec = \buck^{(0)}, \kMapParam{\wVec} = \gVt{(k) }1\}\rightarrow T_3 \in [0, 2^{\numTup - rank(\matrixH')}] \end{equation*} \begin{equation*} T_4 = \gVt{(k \cdot)} | \{\wVec \st \matrixH \cdot \wVec = \buck^{(1)}, \kMapParam{\wVec} = \gVt{(k) 1}\}\rightarrow T_4 \in [0, 2^{\numTup - rank(\matrixH')}]