Crosscorrelation of Rudin-Shapiro-Like Polynomials

Katz, Daniel; Lee, Sangman; Trunov, Stanislav A.

doi:10.48550/arxiv.1702.07697

Cited by 2 publications

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“…( 7)] that modest appending can be used to produce families of sequence pairs with asymptotic PSC slightly lower than 7/6. Katz, Lee, and Trunov crosscorrelated pairs of Rudin-Shapiro-like polynomials [28,Theorem 2.4], by beginning with two different seeds, f 0 and g 0 , and applying recursion (22) to produce two stems f 0 , f 1 , . .…”

Section: Pairs With Low Asymptotic Pursley-sarwate Criterionmentioning

confidence: 99%

Sequences with Low Correlation

Katz

2018

Arithmetic of Finite Fields

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Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in applications. We consider the problem of constructing pairs (f, g) of sequences such that both f and g have low mean square autocorrelation and f and g have low mean square mutual crosscorrelation. We focus on aperiodic correlation of binary sequences, and review recent contributions along with some historical context.

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Section: Pairs With Low Asymptotic Pursley-sarwate Criterionmentioning

confidence: 99%

Sequences with Low Correlation

Katz

2018

Arithmetic of Finite Fields

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“…Correlation is related to norms on the complex unit circle, for example, see the introduction of [2]. So we adopt the convention that if a(z) = j∈Z a j z j is a Laurent polynomial in C[z, z −1 ], then a(z) = j∈Z a j z −j .…”

Section: Proof Of Theorem 11mentioning

confidence: 99%

Sequence Pairs with Lowest Combined Autocorrelation and Crosscorrelation

Katz¹,

Moore²

2017

Preprint

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For a pair (f, g) of sequences of length ℓ whose terms are in {−1, 1}, Pursley and Sarwate established a lower bound on a combined measure of crosscorrelation and autocorrelation for f and g. They showed that the sum of the mean square crosscorrelation between f and g and the geometric mean of f 's mean square autocorrelation and g's mean square autocorrelation must be at least 1. For randomly selected binary sequences, this quantity is typically about 2. In this paper, we show that Pursley and Sarwate's bound is met precisely when (f, g) is a Golay complementary pair. This result generalizes to sequences whose terms are arbitrary complex numbers.

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Crosscorrelation of Rudin-Shapiro-Like Polynomials

Cited by 2 publications

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Sequences with Low Correlation

Sequences with Low Correlation

Sequence Pairs with Lowest Combined Autocorrelation and Crosscorrelation

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