Abstract
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.
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Jedwab, J., Schmidt, KU. (2010). Appended m-Sequences with Merit Factor Greater than 3.34. In: Carlet, C., Pott, A. (eds) Sequences and Their Applications – SETA 2010. SETA 2010. Lecture Notes in Computer Science, vol 6338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15874-2_17
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DOI: https://doi.org/10.1007/978-3-642-15874-2_17
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