The origin of all 4-phase Golay sequences and Golay sequence pairs of even length at most 26 is explained. The principal techniques are the three-stage construction of Fiedler, Jedwab and Parker [FJP08] involving multi-dimensional Golay arrays, and a “sum-difference” construction that modifies a result due to Eliahou, Kervaire and Saffari [EKS91]. The existence of 4-phase seed pairs of lengths ...

A 4-phase Golay sequence pair of length s ≡ 5 (mod 8) is constructed from a Barker sequence of the same length whose even-indexed elements are prescribed. This explains the origin of the 4-phase Golay seed pairs of length 5 and 13. The construction cannot produce new 4-phase Golay sequence pairs, because there are no Barker sequences of odd length greater than 13. A partial converse to the cons...

The cost of detecting asymptomatic colonic cancer with a sequence of occult blood tests by the guaiac method is investigated to determine theelfect of sequence length. The results are sensitive to the definition of a screen positive and a variety of definitions of a positive screen are investigated. It is found that additional tests, when practical, can be used elfectively to reduce the average...

general, any n-sequence determines a multiset of (= n!/k!(n-k)!) k-sequences. "J Suppose, conversely, that we are given a multiset 01 k-sequences. Does that multiset come from some sequence? If so, is the source sequence unique? Such questions are reminiscent of the problem of reconstructing graphs from vertex-deleted sub raphs, which has received a great deal of attention in the last twent yea...

Proteins of the same functional family (for example, kinases) may have significantly different lengths. It is an open question whether such variation in length is random or it appears as a response to some unknown evolutionary driving factors. The main purpose of this paper is to demonstrate existence of factors affecting prokaryotic gene lengths. We believe that the ranking of genomes accordin...

The run vector of a binary sequence reflects the run structure of the sequence, which is given by the set of all substrings of the run length encoding. The run vector and the aperiodic autocorrelations of a binary sequence are strongly related. In this paper, we analyze the run vector of skew-symmetric binary sequences. Using the derived results we present a new and different proof that there e...

A segmentation algorithm based on the Jensen-Shannon entropic divergence is used to decompose longrange correlated DNA sequences into statistically significant, compositionally homogeneous patches. By adequately setting the significance level for segmenting the sequence, the underlying power-law distribution of patch lengths can be revealed. Some of the identified DNA domains were uncorrelated,...

Four Turyn type sequences of lengths 36, 36, 36, 35 are found by a computer search. These sequences give new base sequences of lengths 71, 71, 36, 36 and are used to generate a number of new T -sequences. The first order of many new Hadamard matrices constructible using these new T -sequences is 428.