The Multi-Dimensional Aperiodic Merit Factor of Binary Sequences

Construction of New Asymptotic Classes of Binary Sequences Based on Existing Asymptotic Classes

In this paper, we first demonstrate on optimally shifted Legendre sequences that an addition of a ±1 to the front of all binary sequences belonging to that class does not change the asymptotic value of the aperiodic merit factor. We then extend this result to a general case, showing that concatenation of a ±1 to the front of all sequences belonging to any asymptotic class does not affect the as...

What can be used instead of a Barker sequence ?

A classical problem of digital sequence design, first studied in the 1950s but still not well understood, is to determine long binary sequences for which the absolute values of the aperiodic autocorrelations are collectively as small as possible. The ideal sequence from this point of view is a Barker sequence, but there is overwhelming evidence that no Barker sequence of length greater than 13 ...

Binary Sequences with Asymptotic Aperiodic Merit Factor > 6.3

Advances in the merit factor problem for binary sequences

The identification of binary sequences with large merit factor (small mean-squared aperiodic autocorrelation) is an old problem of complex analysis and combinatorial optimization, with practical importance in digital communications engineering and condensed matter physics. We establish the asymptotic merit factor of several families of binary sequences and thereby prove various conjectures, exp...

Aperiodic correlations and the merit factor of a class of binary sequences

and conjectured that F I 12.32, for all binary sequences, with the exception of the Barker sequence of length 13, for which F = 14.08. In a recent paper Golay [5] argued that the merit factor of Legendre sequences, shifted by one quarter of their lengths, has the highly probable asymptotic value 6, but he did not prove this. For maximal-length shift register sequences, one can see from [6] that...