Papers › On Binary de Bruijn Sequences from LFSRs with Arbitrary Characteristic Polynomials
On Binary de Bruijn Sequences from LFSRs with Arbitrary Characteristic Polynomials
Zuling Chang, Martianus Frederic Ezerman, San Ling, Huaxiong Wang
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We propose a construction of de Bruijn sequences by the cycle joining method from linear feedback shift registers (LFSRs) with arbitrary characteristic polynomial f(x). We study in detail the cycle structure of the set Ω(f(x)) that contains all sequences produced by a specific LFSR on distinct inputs and provide a fast way to find a state of each cycle. This leads to an efficient algorithm to find all conjugate pairs between any two cycles, yielding the adjacency graph. The approach is practical to generate a large class of de Bruijn sequences up to order n ≈20. Many previously proposed constructions of de Bruijn sequences are shown to be special cases of our construction.
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