2009
DOI: 10.1016/j.disc.2008.02.024
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A trace representation of binary Jacobi sequences

Abstract: We determine the trace function representation, or equivalently, the Fourier spectral sequences of binary Jacobi sequences of period pq, where p and q are two distinct odd primes. This includes the twin-prime sequences of period p(p + 2) whenever both p and p + 2 are primes, corresponding to cyclic Hadamard difference sets.

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Cited by 26 publications
(14 citation statements)
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“…If p, q are twin primes then the two prime generator has best possible autocorrelation properties [5] (for the trace representation of the binary two prime gernerator we refer to [3]). In [11] Li et al determined the autocorrelation of the pq-periodic binary cyclotomic sequence T defined by t n = l n if n ∈ Z * pq , where l n is the nth term of the q-periodic Legendre sequence, t n = 0 for n ∈ Q ∪ R and t n = 1 for n ∈ P. It turns out that A(T, t) is not small for a large number of shifts t for all choices of the primes p, q.…”
Section: Discussionmentioning
confidence: 99%
“…If p, q are twin primes then the two prime generator has best possible autocorrelation properties [5] (for the trace representation of the binary two prime gernerator we refer to [3]). In [11] Li et al determined the autocorrelation of the pq-periodic binary cyclotomic sequence T defined by t n = l n if n ∈ Z * pq , where l n is the nth term of the q-periodic Legendre sequence, t n = 0 for n ∈ Q ∪ R and t n = 1 for n ∈ P. It turns out that A(T, t) is not small for a large number of shifts t for all choices of the primes p, q.…”
Section: Discussionmentioning
confidence: 99%
“…h Lemma 2 indicates that the sequence fsðtÞg has two component sequences fb q ðtÞg and fb ðqÞ p ðtÞg. For these two component sequences, we have Lemma 3 [5]. The defining pairs of the two component sequences of fsðtÞg in Lemma 2 are given in Table 2.…”
Section: Defining Pair Of the Generalized Cyclotomic Sequencementioning
confidence: 98%
“…Lemma 6 [5]. A complete set S of representatives of conjugacy classes of the ðp À 1Þðq À 1Þ primitive pqth roots of unity over GFð2Þ is given as…”
Section: Trace Representation Of the Generalized Cyclotomic Sequencementioning
confidence: 99%
“…In particular, for any order d( 2), exact formulas for the periodic autocorrelation values have been computed by the theory of character sums in [17]. A trace representation of W-GCS-I has been presented in [14].…”
Section: Order D and Of Length Pq Which Is Called W-gcs-i Is Definementioning
confidence: 99%