Cross-correlation of binary m and GMW arrays

Sequences and arrays with good auto and cross-correlation are useful in communications and digital watermarking respectively. Two-valued autocorrelation is relatively easy to achieve. However, sets of pseudonoise sequences with good cross-correlation are small and difficult to find. Here, the cross-correlation for particular shifts of m-sequences and GMW sequences is analysed by looking at these sequences as two-dimensional arrays. The particular shifts are natural in the context of the array decomposition. "square" arrays and arrays where the column length is 3 yield now results for m-sequences. The array interpretation also determines the conditions under which the cross-correlation of GMW sequences is identical to the cross-correlation of the m-sequences used in the construction of the GMW pair, enabling known results for m-sequences to be applied. Then GMW sequence pairs with low cross-correlation can be selected.