Mapping prefer-opposite to prefer-one de Bruijn sequences
Des. Codes Cryptography(2016)
摘要
We present a mapping of the binary prefer-opposite de Bruijn sequence of order n onto the binary prefer-one de Bruijn sequence of order n-1 . The mapping is based on the differentiation operator D(⟨b_1,… ,b_l⟩ ) = ⟨ b_2-b_1, b_3-b_2,… , b_l-b_l-1⟩ where bit subtraction is modulo two. We show that if we take the prefer-opposite sequence ⟨b_1,b_2,… ,b_2^n⟩ , apply D to get the sequence ⟨b̂_1, … , b̂_2^n-1⟩ and drop all the bits b̂_i such that ⟨b̂_i,… ,b̂_i+n-1⟩ is a substring of ⟨b̂_1,… ,b̂_i+n-2⟩ , we get the prefer-one de Bruijn sequence of order n-1 .
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关键词
De Bruijn sequences,Prefer one,Prefer opposite,68R15,68R10,05A05
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