By using the Hamilton-Jacobi [$HJ$] framework the higher-order Maxwell-Chern-Simons theory is analyzed. The complete set of $HJ$ Hamiltonians and a generalized $HJ$ differential are reported, from which all symmetries of the theory are identified. In addition, we complete our study by performing the higher order Gitman-Lyakhovich-Tyutin [$GLT$] framework and compare the results of both formalisms.
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