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A binary modified de Bruijn sequence is an infinite and periodic binarysequence derived by removing a zero from the longest run of zeros in a binaryde Bruijn sequence. The minimal polynomial of the modified sequence is itsunique least-degree characteristic polynomial. Leveraging on a recentcharacterization, we devise a novel general approach to determine the minimalpolynomial. We translate the characterization into a problem of identifying aHamiltonian cycle in a specially constructed graph. Along the way, wedemonstrate the usefullness of computational tools from the cycle joiningmethod in the modified setup.

A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences