Linear span of extended sequences and cascaded GMW sequences

In this correspondence, the linear span of extended sequences of period 2/sup em/-1 which are constructed from the ideally correlated sequences of period of 2/sup m/-1 is derived. It is also shown that the linear span of cascaded Gordon-Mills-Welch (GMW) sequences can be derived in the same context. As examples, the linear span of extended Legendre sequences and cascaded GMW sequences with triple trace are computed.