De Bruijn Sequence Generator

A de Bruijn sequence B(k,n) over alphabet size k is a cyclic sequence in which every possible substring of length n appears exactly once. Length = kⁿ. Equivalent to a Hamiltonian cycle on the de Bruijn graph. Used in DNA sequencing (universal library), combinatorics on words, and LFSR design.

Parameters

De Bruijn graph:
Nodes = (n-1)-grams
Edges = n-grams

Construction:
Hierholzer's algorithm
finds Eulerian circuit

Length: kⁿ symbols
DNA use: universal
primer coverage

LFSR: maximal length
shift register IS
a de Bruijn sequence