Pseudo-random sequences and arrays

Abstract

Binary sequences of length n = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> - 1 whose autocorrelation function is either 1 or -1/n have been known for a long time, and are called pseudo-random (or PN) sequences, or maximal-length shift-register sequences. Two-dimensional arrays of area n = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">lm</sup> - 1 with the same property have rcently been found by several authors. This paper gives a simple description of such sequences and arrays and their many nice properties.