A New Class of Binary Sequence Family with Low Correlation and Large Linear Complexity

Qi, Wei

doi:10.1109/iwsda.2007.4408414

Cited by 3 publications

(6 citation statements)

References 14 publications

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“…We comment that a different proof of the above result is in [8]. From Lemma 5.5, we find that the cross correlation of any two sequences in the constructed family is related to C a (e j+s −e j +r).…”

mentioning

confidence: 79%

“…We observe that the number of zeros in each sequence from the constructed family is independent of the chosen shift sequence e. The purpose for adding strong conditions on e is to get the desired correlation property. Wang and Qi [8] give the balance property of the interleaved construction with two Legendre sequences of twin prime periods p and p + 2, respectively. However, there are some typos in their result.…”

Section: Balance Propertymentioning

confidence: 99%

“…In fact, this construction can generate v + 1 sequences so that we have a (v 2 , v + 1, 2v + 3) signal set (see page 364 in [3]). For = 2, Wang and Qi [8] employed Legendre sequences with twin prime periods p ≡ 3 ( mod 4) and p + 2 to construct a (p(p + 2), p + 3, 3p + 4) signal set, and the balance property of such family was also studied.…”

Section: Introductionmentioning

confidence: 99%

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A family of binary sequences from interleaved construction and their cryptographic properties

He¹,

Panario²,

Wang³

2010

Finite Fields: Theory and Applications

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Families of pseudorandom sequences with low cross correlation have important applications in communications and cryptography. Among several known constructions of sequences with low cross correlations, interleaved constructions proposed by Gong uses two sequences of the same period with two-level autocorrelation. In this paper, we study the balance property and the cross correlation of interleaved sequences such that the base sequences may not have the same period, or they may not have two-level autocorrelation. In particular, we study the interleaved sequences of two Legendre sequences of periods p and q, respectively, where p and q are odd prime numbers.

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mentioning

confidence: 79%

Section: Balance Propertymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A family of binary sequences from interleaved construction and their cryptographic properties

He¹,

Panario²,

Wang³

2010

Finite Fields: Theory and Applications

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“…We comment that a different proof of the above result is in [88]. Lemma 4.6 shows that the cross correlation of any two sequences in the constructed family is related to C a (e j+s −e j +r).…”

Section: The Correlation Values Of Binary Interleaved Sequencesmentioning

confidence: 95%

“…We observe that the number of zeros in each sequence from the constructed family is independent of the chosen shift sequence e. The purpose for adding strong conditions on e is to get a desired correlation property. Wang and Qi [88] give the balance property of the interleaved construction with two Legendre sequences of twin prime periods p and p + 2, respectively. However, there are some typos in their result.…”

Section: A New Variant Of the Interleaved Algorithmmentioning

confidence: 99%

Interleaved Sequences Over Finite Fields

He¹

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Chapter 1. Introduction 1.1. Motivation 1.2. Overview of new results Chapter 2. Preliminaries 2.1. Sequences and cryptographic properties 2.2. Maximal length sequences 2.3. Construction of GMW sequences by interleaved approach 2.4. Character sums over finite fields 2.5. Costas sequences 2.6. Some well-known signal sets (families) Chapter 3. Interleaved sequences 3.1. (f (x), m)-interleaved sequences 3.2. IRI-sequences 3.3. Signal sets (families) generated by (f (x), m)−sequences 3.4. A new variant of the interleaved algorithm Chapter 4. Correlation properties and linear complexity of interleaved binary sequences 4.1. Correlation property 4.2. The correlation values of binary interleaved sequences 4.3. Linear complexity of binary interleaved sequences Chapter 5. Linear complexity profile, correlation measures and nonlinearity v vi 5.1. Linear complexity profile of m-ary interleaved sequences 5.2. Relating linear complexity profile and (power) correlation measures 5.3. Nonlinearity of the boolean function derived from binary interleaved sequences Chapter 6. Zero correlation zone of interleaved polyphase sequences 6.1. A new class of almost perfect sequences 6.2. Interleaved construction of polyphase sequences 6.3. A Zero-Correlation Zone (ZCZ) signal set (family) Chapter 7. Shift-addition construction 7.1. Shift and add property and shift-addition construction 7.2. Shift-addition family from m-ary power residue sequences 7.3. Shift-addition family from two-prime generators of order 2 Chapter 8. Future work Bibliography CHAPTER 1

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Investigation of the Correlation Properties of Spreading Sequences for Asynchronous CDMA

Кuznetsov

Krasnobaev

Bagmut

et al. 2021

2021 11th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applicat

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A New Class of Binary Sequence Family with Low Correlation and Large Linear Complexity

Cited by 3 publications

References 14 publications

A family of binary sequences from interleaved construction and their cryptographic properties

A family of binary sequences from interleaved construction and their cryptographic properties

Interleaved Sequences Over Finite Fields

Investigation of the Correlation Properties of Spreading Sequences for Asynchronous CDMA

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