De Bruijn Sequence - Construction

Construction

The De Bruijn sequences can be constructed by taking a Hamiltonian path of an n-dimensional De Bruijn graph over k symbols (or equivalently, a Eulerian cycle of a (n − 1)-dimensional De Bruijn graph), or via finite fields.

An alternative construction involves concatenating together, in lexicographic order, all the Lyndon words whose length divides n.

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