The merit factor of long low autocorrelation binary sequences (Corresp.)

Abstract

The asymptotic "merit factor," i.e, the ratio of central to sidelobe energy of extremely long, optimally Iow autocorrelation sequences, formerly calculated as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2e^{2}=14.778 \cdots</tex> with the use of an ergodicity hypothesis and a convenient, but faulty, approximation, is recalculated without that approximation and is established at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12.32 \cdots</tex> .