Binary sequences with high linear complexity are of interest in cryptography. The linear complexity should remain high even when a small number of changes are made to the sequence. The error linear complexity spectrum of a sequence reveals how the linear complexity of the sequence varies as an increasing number of the bits of the sequence are changed. We present an algorithm which computes the ...

Binary information is prevalent in the environment and contains 2 distinct outcomes. Binary sequences consist of a mixture of alternation and repetition. Understanding how people perceive such sequences would contribute to a general theory of information processing. In this study, we examined how people process alternation and repetition in binary sequences. Across 4 paradigms involving estimat...

Low autocorrelation binary sequences (LABS) are very important for communication applications. And it is a notoriously difficult computational problem to find binary sequences with low aperiodic autocorrelations. The problem can also be stated in terms of finding binary sequences with minimum energy levels or maximum merit factor defined by M.J.E. Golay, E N F 2 2 = , N and E being the sequence...

R. L. Graham and H. O. Pollak observed that the sequence u1 = 1, un+1 = ⌊√ 2 ( un + 1 2 )⌋ , n ≥ 1, has the curious property that the sequence of numbers (u2n+1 − 2u2n−1)n≥1 gives the binary digits of √ 2. We present an extension of the Graham–Pollak sequence which allows to get – in a fancy way – the binary digits of 759250125 √ 2 and other numbers.

R. L. Graham and H. O. Pollak observed that the sequence u1 = 1, un+1 = ⌊ √ 2 (un + 1/2)⌋, n ≥ 1, has the curious property that the sequence of numbers (u2n+1−2u2n−1)n≥1 denotes the binary digits of √ 2. We present an extension of Graham–Pollak’s sequence which allows to get – in a fancy way – the binary digits of 759250125 √ 2 and other numbers.

We analyse a binary cyclotomic sequence constructed via generalized cyclotomic classes by Bai et al. (IEEE Trans Inforem Theory 51: 1849–1853, 2005). First we determine the linear complexity of a natural generalization of this binary sequence to arbitrary prime fields. Secondly we consider k-error linear complexity and autocorrelation of these sequences and point out certain drawbacks of this c...

The peak sidelobe level (PSL) of a binary sequence is the largest absolute value of all its nontrivial aperiodic autocorrelations. A classical problem of digital sequence design is to determine how slowly the PSL of a length n binary sequence can grow, as n becomes large. Moon and Moser showed in 1968 that the growth rate of the PSL of almost all length n binary sequences lies between order √ n...