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The $(c,k)$-Load Coloring Problem (denoted $(c,k)$-LCP) asks whether there is a $c$-coloring $\\varphi: V \\rightarrow [c]$ such that for every $i \\in [c]$, there are at least $k$ edges with both endvertices colored $i$. Gutin and Jones (IPL 2014) studied this problem with $c=2$. They showed $(2,k)$-LCP to be fixed parameter tractable (FPT) with parameter $k$ by obtaining a kernel with at most $7k$ vertices. In this paper, we extend the study to any fixed $c$ by giving both a linear-vertex and a linear-edge kernel. 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