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Enumeration and criteria for cyclically shift-distinct GMW sequences

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3 Author(s)
Guang Gong ; Dept. of Combinatorics & Optimization, Waterloo Univ., Ont., Canada ; Zong-Duo Dai ; Golomb, S.W.

Gordon-Mills-Welch (GMW) sequences (also called cascaded GMW sequences) have two-level autocorrelations. This property makes them widely used in various communication and cryptographic systems. The generation of q-ary GMW sequences of period qn-1 involves three types of parameters. To determine whether GMW sequences are cyclically shift-distinct for differing parameters has remained an open question until now. In this paper, we completely solve this problem for varying all three types of parameters. We find a criterion for cyclically shift-distinct q-ary GMW sequences of period qn-1, and obtain the number of such sequences. For the special case of q=2, this solution facilitates counting the number of cyclic Hadamard difference sets which correspond to binary GMW sequences of period 2n-1

Published in:

Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 2 )

Date of Publication:

Mar 2000

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