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We explicitly construct a genus-$3$ Lefschetz fibration over $\mathbb{S}^{2}$whose total space is $\mathbb{T}^{2}\times \mathbb{S}^{2}\#6\overline{\mathbb{C} P^{2}}$ using the monodromy of Matsumoto's genus-$2$Lefschetz fibration. We then construct more genus-$3$ Lefschetz fibrationswhose total spaces are exotic minimal symplectic $4$-manifolds $3 \mathbb{C}P^{2} \# q\overline{\mathbb{C} P^{2}}$ for $q=13,\ldots,19$. We also generalizeour construction to get genus-$3k$ Lefschetz fibration structure on the$4$-manifold $\Sigma_{k}\times \mathbb{S}^{2}\# 6\overline{\mathbb{C} P^{2}}$using the generalized Matsumoto's genus-$2k$ Lefschetz fibration. From thisgeneralized version, we derive further exotic $4$-manifolds via Luttingersurgery and twisted fiber sum.

Genus-$3$ Lefschetz Fibrations and Exotic $4$-Manifolds with $b_{2}^{+}=3$