IEEE Transactions on Information Theory, ISSN 0018-9448, 06/2015, Volume 61, Issue 6, pp. 3276 - 3304

We give a new existence criterion for p-ary sequences which have ideal two-level autocorrelation; and we use it to obtain four general families of such...

Context | Correlation | Fourier transforms | Additives | Convolution | relative difference set | ideal two-level autocorrelation | Polynomials | p-ary sequence | character sum | Stickelberger congruence | Gauss sum | p-Ary sequence | Character sum | SINGER PARAMETERS | COMPUTER SCIENCE, INFORMATION SYSTEMS | CYCLIC DIFFERENCE SETS | FAMILY | ENGINEERING, ELECTRICAL & ELECTRONIC | Sequences (Mathematics) | Coding theory | Research | Correlation (Statistics) | Factorials | Mathematical research

Context | Correlation | Fourier transforms | Additives | Convolution | relative difference set | ideal two-level autocorrelation | Polynomials | p-ary sequence | character sum | Stickelberger congruence | Gauss sum | p-Ary sequence | Character sum | SINGER PARAMETERS | COMPUTER SCIENCE, INFORMATION SYSTEMS | CYCLIC DIFFERENCE SETS | FAMILY | ENGINEERING, ELECTRICAL & ELECTRONIC | Sequences (Mathematics) | Coding theory | Research | Correlation (Statistics) | Factorials | Mathematical research

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 11/2002, Volume 48, Issue 11, pp. 2847 - 2867

New designs for families of sequences over GF(p) with low cross correlation, balance property, and large linear span are presented. The key idea of the new...

Galois fields | Correlation | Binary sequences | Low cross correlation | Nonbinary sequences | Finite field | Interleaved sequences | Linear span | Two-level autocorrelation | low cross correlation | IDEAL AUTOCORRELATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | BINARY PSEUDORANDOM SEQUENCES | two-level autocorrelation | ENGINEERING, ELECTRICAL & ELECTRONIC | linear span | interleaved sequences | finite field | 2-LEVEL AUTOCORRELATION FUNCTION | CASCADED GMW SEQUENCES | LARGE FAMILIES | PERIODIC CORRELATION-PROPERTIES | nonbinary sequences | Electrical engineering | Research | Information theory | Autocorrelation (Statistics) | Autocorrelation functions | Residues | Balancing | Cross correlation | Hardware | Autocorrelation | Optimization | Computer programs

Galois fields | Correlation | Binary sequences | Low cross correlation | Nonbinary sequences | Finite field | Interleaved sequences | Linear span | Two-level autocorrelation | low cross correlation | IDEAL AUTOCORRELATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | BINARY PSEUDORANDOM SEQUENCES | two-level autocorrelation | ENGINEERING, ELECTRICAL & ELECTRONIC | linear span | interleaved sequences | finite field | 2-LEVEL AUTOCORRELATION FUNCTION | CASCADED GMW SEQUENCES | LARGE FAMILIES | PERIODIC CORRELATION-PROPERTIES | nonbinary sequences | Electrical engineering | Research | Information theory | Autocorrelation (Statistics) | Autocorrelation functions | Residues | Balancing | Cross correlation | Hardware | Autocorrelation | Optimization | Computer programs

Journal Article

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, ISSN 0916-8508, 2010, Volume E93-A, Issue 11, pp. 2278 - 2285

Binary sequence pairs as a class of mismatched filtering of binary sequences can be applied in radar sonar and spread spectrum communication system Binary...

Two-level periodic autocorrelation function | Binary sequence pair | Sequence pair with zero correlation zone | Difference set pair | difference set pair | sequence pair with zero | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ZERO-CORRELATION ZONE | COMPUTER SCIENCE, INFORMATION SYSTEMS | correlation zone | binary sequence pair | two level periodic autocorrelation function | ENGINEERING, ELECTRICAL & ELECTRONIC | Autocorrelation functions | Construction | Equivalence | Digital signal processing | Electronics | Binary systems | Mathematical models | Combinatorial analysis

Two-level periodic autocorrelation function | Binary sequence pair | Sequence pair with zero correlation zone | Difference set pair | difference set pair | sequence pair with zero | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ZERO-CORRELATION ZONE | COMPUTER SCIENCE, INFORMATION SYSTEMS | correlation zone | binary sequence pair | two level periodic autocorrelation function | ENGINEERING, ELECTRICAL & ELECTRONIC | Autocorrelation functions | Construction | Equivalence | Digital signal processing | Electronics | Binary systems | Mathematical models | Combinatorial analysis

Journal Article

Journal of Theoretical and Applied Information Technology, ISSN 1992-8645, 2013, Volume 52, Issue 1, pp. 51 - 56

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 08/2014, Volume 60, Issue 8, pp. 5054 - 5064

In 1998, Lin presented a conjecture on a class of ternary sequences with ideal two-level autocorrelation. Those sequences have a very simple structure, i.e.,...

Multiplexing | Correlation | Transforms | Educational institutions | Polynomials | Cryptography | Hamming weight | Teichmüller character | two-level autocorrelation | Stickelberger's theorem | multiplexing decimation-Hadamard transform | decimation-Hadamard transform | Teichmuller character | 2-LEVEL AUTOCORRELATION SEQUENCES | SINGER PARAMETERS | IDEAL AUTOCORRELATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | BINARY PSEUDORANDOM SEQUENCES | CYCLIC DIFFERENCE SETS | ENGINEERING, ELECTRICAL & ELECTRONIC | Hamming code | Hadamard matrices | Usage | Analysis | Digital multiplexing | Multichannel communication | Sequences | Equivalence | Mathematical analysis | Proving | Byproducts | Autocorrelation | Combinatorial analysis

Multiplexing | Correlation | Transforms | Educational institutions | Polynomials | Cryptography | Hamming weight | Teichmüller character | two-level autocorrelation | Stickelberger's theorem | multiplexing decimation-Hadamard transform | decimation-Hadamard transform | Teichmuller character | 2-LEVEL AUTOCORRELATION SEQUENCES | SINGER PARAMETERS | IDEAL AUTOCORRELATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | BINARY PSEUDORANDOM SEQUENCES | CYCLIC DIFFERENCE SETS | ENGINEERING, ELECTRICAL & ELECTRONIC | Hamming code | Hadamard matrices | Usage | Analysis | Digital multiplexing | Multichannel communication | Sequences | Equivalence | Mathematical analysis | Proving | Byproducts | Autocorrelation | Combinatorial analysis

Journal Article

Journal of Russian Laser Research, ISSN 1071-2836, 5/2011, Volume 32, Issue 3, pp. 269 - 276

We study the statistics of the emitted light from a single two-level atom in a cavity. We explore the effects of counter-rotating terms. We show that the...

Microwaves, RF and Optical Engineering | autocorrelation function | Optics, Optoelectronics, Plasmonics and Optical Devices | Laser Technology, Photonics | Physics | two-level system | Autocorrelation functions | Holes | Emittance | Lasers | Statistics

Microwaves, RF and Optical Engineering | autocorrelation function | Optics, Optoelectronics, Plasmonics and Optical Devices | Laser Technology, Photonics | Physics | two-level system | Autocorrelation functions | Holes | Emittance | Lasers | Statistics

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2006, Volume 154, Issue 18, pp. 2590 - 2598

Let be a prime, and be the finite field with elements. In this paper, we will consider -ary sequences of period for and study their various balance properties:...

Non-binary PN sequences | Cyclic difference sets with singer type parameters | Two-tuple-balance property | Balance property | Array structure | Difference-balance property | Ideal two-level autocorrelation | MATHEMATICS, APPLIED | cyclic difference sets with singer type parameters | balance property | ideal two-level autocorrelation | two-tuple-balance property | CASCADED GMW SEQUENCES | non-binary PN sequences | difference-balance property | array structure

Non-binary PN sequences | Cyclic difference sets with singer type parameters | Two-tuple-balance property | Balance property | Array structure | Difference-balance property | Ideal two-level autocorrelation | MATHEMATICS, APPLIED | cyclic difference sets with singer type parameters | balance property | ideal two-level autocorrelation | two-tuple-balance property | CASCADED GMW SEQUENCES | non-binary PN sequences | difference-balance property | array structure

Journal Article

IEEE TRANSACTIONS ON INFORMATION THEORY, ISSN 0018-9448, 08/2014, Volume 60, Issue 8, pp. 5054 - 5064

In 1998, Lin presented a conjecture on a class of ternary sequences with ideal two-level autocorrelation. Those sequences have a very simple structure, i.e.,...

Stickelberger's theorem | 2-LEVEL AUTOCORRELATION SEQUENCES | Teichmuller Character | SINGER PARAMETERS | IDEAL AUTOCORRELATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | BINARY PSEUDORANDOM SEQUENCES | CYCLIC DIFFERENCE SETS | two-level autocorrelation | multiplexing decimation-Hadamard transform | decimation-Hadamard transform | ENGINEERING, ELECTRICAL & ELECTRONIC

Stickelberger's theorem | 2-LEVEL AUTOCORRELATION SEQUENCES | Teichmuller Character | SINGER PARAMETERS | IDEAL AUTOCORRELATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | BINARY PSEUDORANDOM SEQUENCES | CYCLIC DIFFERENCE SETS | two-level autocorrelation | multiplexing decimation-Hadamard transform | decimation-Hadamard transform | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Dianzi Yu Xinxi Xuebao/Journal of Electronics and Information Technology, ISSN 1009-5896, 05/2012, Volume 34, Issue 5, pp. 1174 - 1178

Journal Article

Journal of Russian Laser Research, ISSN 1071-2836, 05/2011, Volume 32, Issue 3, pp. 269 - 276

We study the statistics of the emitted light from a single two-level atom in a cavity. We explore the effects of counter-rotating terms. We show that the...

autocorrelation function | two-level system | RESONANCE FLUORESCENCE | LIFETIMES | MICROCAVITY-EMITTING FIELD | PHOTON | QUANTUM | CAVITY | NOISE | OPTICS

autocorrelation function | two-level system | RESONANCE FLUORESCENCE | LIFETIMES | MICROCAVITY-EMITTING FIELD | PHOTON | QUANTUM | CAVITY | NOISE | OPTICS

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2002, Volume 48, Issue 4, pp. 853 - 865

A new method to study and search for two-level autocorrelation sequences for both binary and nonbinary cases is developed. This method iteratively applies two...

Correlation | Trace representation | Group characters | Iterative decimation-Hadamard transform (DHT) | Two-level autocorrelation sequences | Orthogonal functions | group characters | IDEAL AUTOCORRELATION | BINARY | COMPUTER SCIENCE, INFORMATION SYSTEMS | orthogonal functions | iterative decimation-Hadamard transform (DHT) | trace representation | two-level autocorrelation sequences | ENGINEERING, ELECTRICAL & ELECTRONIC | Research | Information theory | Searching | Transforms | Autocorrelation | Factorization | Counting

Correlation | Trace representation | Group characters | Iterative decimation-Hadamard transform (DHT) | Two-level autocorrelation sequences | Orthogonal functions | group characters | IDEAL AUTOCORRELATION | BINARY | COMPUTER SCIENCE, INFORMATION SYSTEMS | orthogonal functions | iterative decimation-Hadamard transform (DHT) | trace representation | two-level autocorrelation sequences | ENGINEERING, ELECTRICAL & ELECTRONIC | Research | Information theory | Searching | Transforms | Autocorrelation | Factorization | Counting

Journal Article

Comptes Rendus de L'Academie Bulgare des Sciences, ISSN 1310-1331, 2011, Volume 64, Issue 7, pp. 917 - 924

In this correspondence, for every periodic p-ary sequence satisfying ideal two-level autocorrelation property the existence of an element of the field GF(p)...

Almost balancedness | Ideal two-level autocorrelation property | almost balancedness | GMW SEQUENCES | ideal two-level autocorrelation property | MULTIDISCIPLINARY SCIENCES

Almost balancedness | Ideal two-level autocorrelation property | almost balancedness | GMW SEQUENCES | ideal two-level autocorrelation property | MULTIDISCIPLINARY SCIENCES

Journal Article

Dianzi Yu Xinxi Xuebao/Journal of Electronics and Information Technology, ISSN 1009-5896, 07/2009, Volume 31, Issue 7, pp. 1536 - 1541

Journal Article

Xi Tong Gong Cheng Yu Dian Zi Ji Shu/Systems Engineering and Electronics, ISSN 1001-506X, 01/2010, Volume 32, Issue 1, pp. 31 - 34

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 7/2001, Volume 23, Issue 2, pp. 157 - 166

Let α be a primitive element of $$F_{3^n } $$ . Letd=32k -3 k +1 wheren=3k. We show that the ternary sequence s(t) given by $$s(t) = Tr_n (\alpha ^t + \alpha...

Information and Communication, Circuits | Data Structures, Cryptology and Information Theory | Convex and Discrete Geometry | Mathematics | Combinatorics | sequences | two-level autocorrelation | ideal autocorrelation | Electronic and Computer Engineering | Sequences | Two-level autocorrelation | Ideal autocorrelation | MATHEMATICS, APPLIED | BINARY PSEUDORANDOM SEQUENCES | COMPUTER SCIENCE, THEORY & METHODS | CYCLIC DIFFERENCE SETS

Information and Communication, Circuits | Data Structures, Cryptology and Information Theory | Convex and Discrete Geometry | Mathematics | Combinatorics | sequences | two-level autocorrelation | ideal autocorrelation | Electronic and Computer Engineering | Sequences | Two-level autocorrelation | Ideal autocorrelation | MATHEMATICS, APPLIED | BINARY PSEUDORANDOM SEQUENCES | COMPUTER SCIENCE, THEORY & METHODS | CYCLIC DIFFERENCE SETS

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 03/1999, Volume 45, Issue 2, pp. 692 - 693

We derive the values of the Fourier spectrum, a decomposition, and an achievable upper bound on the linear span, for binary sequences with two-level...

Upper bound | Codes | Discrete Fourier transforms | Polynomials | Autocorrelation | Hamming weight | Binary sequences | Linear spans of binary sequences | Cyclic hadamard difference sets | Two-level autocorrelation | COMPUTER SCIENCE, INFORMATION SYSTEMS | linear spans of binary sequences | two-level autocorrelation | cyclic Hadamard difference sets | ENGINEERING, ELECTRICAL & ELECTRONIC | Research | Difference equations | Fourier series | Numerical solutions | Autocorrelation (Statistics) | Fourier analysis | Decomposition | Upper bounds | Information theory

Upper bound | Codes | Discrete Fourier transforms | Polynomials | Autocorrelation | Hamming weight | Binary sequences | Linear spans of binary sequences | Cyclic hadamard difference sets | Two-level autocorrelation | COMPUTER SCIENCE, INFORMATION SYSTEMS | linear spans of binary sequences | two-level autocorrelation | cyclic Hadamard difference sets | ENGINEERING, ELECTRICAL & ELECTRONIC | Research | Difference equations | Fourier series | Numerical solutions | Autocorrelation (Statistics) | Fourier analysis | Decomposition | Upper bounds | Information theory

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 08/2018, Volume 64, Issue 8, pp. 5957 - 5960

Hu introduced a simple method to compute the 2-adic complexity of any periodic binary sequence with ideal two-level autocorrelation. We extend this approach to...

Correlation | Legendre sequence | Radon | two-prime generator | 2-adic complexity | Generators | Complexity theory | Electronic mail | two-level autocorrelation | SEQUENCES | ORDER 2 | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Binary system | Complexity

Correlation | Legendre sequence | Radon | two-prime generator | 2-adic complexity | Generators | Complexity theory | Electronic mail | two-level autocorrelation | SEQUENCES | ORDER 2 | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Binary system | Complexity

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 03/2011, Volume 57, Issue 3, pp. 1530 - 1547

Let p = ef + 1 be an odd prime for some e and e and let f, be the finite field with F p elements. In this paper, we explicitly describe the trace...

Correlation | linear complexity | Generators | e th residue cyclic difference sets | Complexity theory | Indexes | Hamming weight | trace representations | Binary sequences with two-level autocorrelation | Polynomials | cyclic difference sets | Binary sequences | minimal polynomials | eth residue cyclic difference sets | EXISTENCE | IDEAL AUTOCORRELATION | HADAMARD DIFFERENCE SETS | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | LEGENDRE SEQUENCES | PSEUDORANDOM SEQUENCES | Sequences (Mathematics) | Research

Correlation | linear complexity | Generators | e th residue cyclic difference sets | Complexity theory | Indexes | Hamming weight | trace representations | Binary sequences with two-level autocorrelation | Polynomials | cyclic difference sets | Binary sequences | minimal polynomials | eth residue cyclic difference sets | EXISTENCE | IDEAL AUTOCORRELATION | HADAMARD DIFFERENCE SETS | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | LEGENDRE SEQUENCES | PSEUDORANDOM SEQUENCES | Sequences (Mathematics) | Research

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 09/2014, Volume 60, Issue 9, pp. 5803 - 5804

We show that there is a very simple approach to determine the 2-adic complexity of periodic binary sequences with ideal two-level autocorrelation. This is the...

Correlation | Transforms | Complexity theory | Teichmuller character | Stickelberger's theorem | COMPUTER SCIENCE, INFORMATION SYSTEMS | two-level autocorrelation | multiplexing decimation-Hadamard transform | decimation-Hadamard transform | ENGINEERING, ELECTRICAL & ELECTRONIC

Correlation | Transforms | Complexity theory | Teichmuller character | Stickelberger's theorem | COMPUTER SCIENCE, INFORMATION SYSTEMS | two-level autocorrelation | multiplexing decimation-Hadamard transform | decimation-Hadamard transform | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Information Sciences, ISSN 0020-0255, 2008, Volume 178, Issue 7, pp. 1903 - 1916

In this paper we present a family of stream ciphers which generate a keystream with ideal two-level autocorrelation. The design also guarantees other...

Randomness properties | Welch–Gong | Two-level autocorrelation | Stream cipher | Welch-Gong | randomness properties | COMPUTER SCIENCE, INFORMATION SYSTEMS | two-level autocorrelation | stream cipher | ALGEBRAIC ATTACKS

Randomness properties | Welch–Gong | Two-level autocorrelation | Stream cipher | Welch-Gong | randomness properties | COMPUTER SCIENCE, INFORMATION SYSTEMS | two-level autocorrelation | stream cipher | ALGEBRAIC ATTACKS

Journal Article

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