Binary sequences with Gold-like correlation but larger linear span

摘要

A new construction of optimal binary sequences, identical to the well known family of Gold sequences in terms of maximum nontrivial correlation magnitude and family size, but having larger linear span is presented. The distribution of correlation values is determined. For every odd integer /spl tau//spl ges/3, the construction provides a family that contains 2/sup /spl tau//+1 cyclically distinct sequences, each of period 2/sup /spl tau//-1. The maximum nontrivial correlation magnitude equals 2(/spl tau/+1)/sup /2/+1, with one exception, each of the sequences in the family has linear span at least (/spl tau//sup 2/-/spl tau/)/2 (compared to 2/spl tau/ for Gold sequences). The sequences are easily implemented using a quaternary shift register followed by a simple feedforward nonlinearity.