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- W2006880019 abstract "The following theorem is proved. Let k be any positive integer and let l be any integer satisfying 1 ≤ l < k and denote by g the greatest common divisor ( k , l ) of k and l . For k and l s.t. ( k , l ) = g = 1 and for any integer m satisfying k 2 > (m − 1) , construct all possible 2 m binary sequences { b 0 , b 1 , b 2 ,…, b k −1 } of length k under the following m equality constraints: b l−1 b 2l−1 b 3l−1 … b k−r 1 b l−r 1 b 2l−1 1 b 3l−r 1 … b k−r 2 b l−r 2 b 2l−r 1 b 3l−r 2 … b k−r 3 b l−r m−1 b 2l−r m−1 b 3l−r m−1 … b k−r 1 where 1. (i) the subscripts are considered modulo- k ; 2. (ii) each “equality chain” ends when its subscript first reaches one of the m integers ( k − 1), ( k − 2),…, ( k − m ), i.e., r i ∈ {2, 3,…, m } for i = 1, 2,…, m − 1; r i ≠ r 3 ( i ≠ j ); and 3. (iii) each b i lies on precisely one of these m equality chains. Then the number of the resulting 2 m binary sequences that are cyclically distinct and have no internal periodicity is 2 m−1 for m ≥ 2 and zero for m = 1. The result has application in the enumeration of shift register sequences." @default.
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- W2006880019 title "On the number of cyclically distinct binary sequences having no internal periodicity and satisfying certain equality constraints" @default.
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- W2006880019 doi "https://doi.org/10.1016/0095-8956(76)90009-5" @default.
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