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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 r [is greater than or equal to] 3, the construction provides a family that contains [2.sup.r] + 1 cyclically distinct sequences, each of period [2.sup.r] - 1. The maximum nontrivial correlation magnitude equals [2.sup.(r+1)/2] + 1. With one exception, each of the sequences in the family has linear span at least ([r.sup.2] - r)/2 (compared to 2r for Gold sequences). The sequences are easily implemented using a quaternary shift register followed by a simple feedforward nonlinearity.