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Complex sequences over GF(pM) with a two-level autocorrelation function and a large linear span

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2 Author(s)
M. Antweiler ; Inst. fuer Elektrische Nachrichtentechnik, Rhein.-Westf. Tech. Hochschule, Aachen, Germany ; L. Bomer

New complex sequences with elements are proposed that have constant absolute values of 1. The periodic autocorrelation functions of these sequences are shown to be two-level. The sequences are generated by three consecutive mapping processes. The number of sequences of fixed length is determined, which is larger than the number of binary sequences. For cryptographical reasons, the large linear span of the sequences is of great interest. The linear span of the new sequences is examined and is proven to be larger than the linear span of complex m-sequences, if the parameters of the mapping processes are appropriately chosen. The formula for generating the sequences is generalized to enlarge the linear span of sequences

Published in:

IEEE Transactions on Information Theory  (Volume:38 ,  Issue: 1 )