New Binary Sequences With Optimal Autocorrelation Magnitude

Abstract

New binary sequences of period N = 4(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> - 1) for even m ges 4 are found, where the sequences are described by a 4 X (2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> - 1) array structure. The new sequences are almost balanced and have four- valued autocorrelation, i.e., {N, 0, plusmn4}, which is optimal with respect to autocorrelation magnitude. The complete autocorrelation distribution and the exact linear complexity of the sequences are mathematically derived. Finally, it is shown that the sequences are implemented by a combination of linear feedback shift registers and a simple logic.