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A new family of Gold-like sequences

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3 Author(s)
Khoongming Khoo ; Centre for Appl. Cryptographic Res., Waterloo Univ., Ont., Canada ; Guang Gong ; Stinson, D.R.

Families of sequences with low cross correlation have important applications in CDMA communications and cryptography. One class of such sequences are those which have period 2n-1 and cross correlation values -1, -1±2 (n+1)2/ with m-sequence represented by Tr(x) when n is odd. These sequences are called Gold-like sequences and they are well studied in the literature, In this paper, we generalise their concept and consider sequences over GF(2n), n odd. Using techniques from linear algebra and coding theory, we can efficiently determine if the sequence is Gold-like by a polynomial gcd computation. Using the tools developed, we prove that the sequence is Gold-like for all choice of coefficients if and only if n is a prime of certain form.

Published in:

Information Theory, 2002. Proceedings. 2002 IEEE International Symposium on

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