Linear complexity of modulo-m related prime sequences

Abstract

The linear complexity of m-phase related prime sequences is investigated for the case when m is composite. For each relatively prime factor pik of m, the linear complexity and the characteristic polynomial of the shortest linear feedback shift register that generates the pik-phase version of the sequence can be deduced and these results can then be combined using the Chinese remainder theorem to derive the m-phase values. These values are shown to depend on the categories of the sequence length computed modulo each factor of m, rather than on the category of the length modulo m itself, and that these values depend on the primitive roots employed. For a given length, the highest values of linear complexity result from constructing the sequences using those values of primitive elements that lead to non-zero categories for each factor of m.