Appended m-Sequences with Merit Factor Greater than 3.34
نویسندگان
چکیده
We consider the merit factor of binary sequences obtained by appending an initial fraction of an m-sequence to itself. We show that, for all sufficiently large n, there is some rotation of each m-sequence of length n that has merit factor greater than 3.34 under suitable appending. This is the first proof that the asymptotic merit factor of a binary sequence family can be increased under appending. We also conjecture, based on numerical evidence, that each rotation of an m-sequence has asymptotic merit factor greater than 3.34 under suitable appending. Our results indicate that the effect of appending on the merit factor is strikingly similar for m-sequences as for rotated Legendre sequences.
منابع مشابه
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...
متن کاملConstruction 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...
متن کاملThe merit factor of binary sequences related to difference sets
Long binary sequences related to cyclic difference sets are investigated. Among all known constructions of cyclic difference sets we show that only sequences constructed from Hadamard difference sets can have an asymptotic nonzero merit factor. Maximal length shift register sequences, Legendre, and twin-prime sequences are all constructed from Hadamard difference sets. We prove that the asympto...
متن کاملThe merit factor of binary sequence families constructed from m-sequences
We consider the asymptotic merit factor of two binary sequence families obtained from an initial binary sequence family using a “negaperiodic” and a “periodic” construction. When the initial sequences are m-sequences, both of the constructed families have the same asymptotic merit factor as the initial family, at all rotations of sequence elements. A similar property was previously shown to hol...
متن کاملTwo binary sequence families with large merit factor
We calculate the asymptotic merit factor, under all rotations of sequence elements, of two families of binary sequences derived from Legendre sequences. The rotation is negaperiodic for the first family, and periodic for the second family. In both cases the maximum asymptotic merit factor is 6. As a consequence, we obtain the first two families of skew-symmetric sequences with known asymptotic ...
متن کامل