Abstract: We have derived the first Noether theorem and Noether identities in canonical formalism for field theory with higher-order singular Lagrangian,which is a powerful tool to analyse Dirac constraint for such system. A gauge-variant system in canonical variables formalism must has Dirac constraint.For a system with first class constraint (FCC), we have developed an algorithm for construction of the gauge generator of such system. An application to the Podolsky generalized electromagnetic field was given.

Key words: Dirac's theory of constrained system, Higher-order singular Lagrangian, Gauge generator