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where the maximum is taken over all D = (d1, . . . , dl) and M such that 0 ≤ d1 < · · · < dl ≤ N −M . The sequence EN is considered to be a “good” pseudorandom sequence if both these measures W (EN ) and Cl(EN ) (at least for small l) are “small” in terms of N (in particular, both are o(N) as N → ∞). This terminology is justified since for a truly random sequence EN each of these measures is √ N logN . (For a more precise version of this result see [1].) Using the Legendre symbol, Mauduit and Sárközy [6] showed an example of a “good” pseudorandom sequence. They defined a binary sequence by putting N = p− 1 where p is a prime number, and

A construction of pseudorandom binary sequences using both additive and multiplicative characters