Results 1 
6 of
6
New Designs for Signal Sets with Low Crosscorrelation, Balance Property and Large Linear Span: GF(p) Case
 IEEE Trans. Inform. Theory
, 2000
"... 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 designs is to use short pary sequences of period v with the 2level auto correlation function to construct a set of long sequences with the des ..."
Abstract

Cited by 14 (6 self)
 Add to MetaCart
(Show Context)
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 designs is to use short pary sequences of period v with the 2level auto correlation function to construct a set of long sequences with the designed properties. The resulting sequences are of interleaved sequences of period v 2 . There are v cyclically shift distinct sequences in each family. The maximal magnitude of cross/outofphase auto correlation of sequences in the family is 2v + 3 which is optimal with respect to the Welch bound. In particular, for binary case, cross/outofphase auto correlation values belong to the set f1; v; v + 2; 2v + 3; 2v 1g. Each sequence in the family is balanced and has large linear span. For binary case, any sequence in such a family where the short sequences are quadratic residue sequences achieves the maximal linear span. For nonbinary case, the new design gives the first type of signal set...
Character Sums and Polyphase Sequence Families with Low Correlation, DFT and Ambiguity
"... We present a survey on the current status of the constructions of polyphase sequences with low correlation, discrete Fourier transform (DFT), and ambiguity in both time and phase domain, including some new insights and results. Firstly, we systematically introduce the concepts of phaseshift operato ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
We present a survey on the current status of the constructions of polyphase sequences with low correlation, discrete Fourier transform (DFT), and ambiguity in both time and phase domain, including some new insights and results. Firstly, we systematically introduce the concepts of phaseshift operators and ambiguity functions of sequences, and give a new construction of polyphase sequences from combinations of different indexing field elements and hybrid characters. We then present the constructions, some known and some new, of polyphase sequences with low degree polynomials, for their low correlation, DFT and ambiguity can be bounded by directly applying the Weil bounds. Thirdly, we introduce the Hadamard equivalence, restate the conjectured new ternary 2level autocorrelation sequences, and present their Hadamard equivalence relations. Some open problems are presented.
New Ternary and Quaternary Sequences with TwoLevel Autocorrelation
"... Pseudorandom sequences with good correlation properties are widely used in communications and cryptography. The search of new sequences with twolevel autocorrelation has been a very interesting problem for decades. In 2002, Gong and Golomb proposed the iterative decimationHadamard transform (DHT) ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Pseudorandom sequences with good correlation properties are widely used in communications and cryptography. The search of new sequences with twolevel autocorrelation has been a very interesting problem for decades. In 2002, Gong and Golomb proposed the iterative decimationHadamard transform (DHT) which is an useful tool to study twolevel autocorrelation sequences. They showed that for all odd n ≤ 17, using the secondorder decimationHadamard transform, and starting with a single binary msequence, all known twolevel autocorrelation sequences of period 2 n − 1 which have no subfield factorization can be obtained. In this paper, we find many new ternary or quaternary sequences with twolevel autocorrelation using the secondorder decimationHadamard transform. The period of such sequences is 2 n − 1. Index Terms. Pseudorandom sequence, ternary sequence, quaternary sequence, twolevel autocorrelation, iterative decimationHadamard transform (DHT), Dobbertin’s polynomial. 1
1 On a Connection between Ideal Twolevel Autocorrelation and Almost Balancedness of pary Sequences*
"... ar ..."
(Show Context)
The Proof of Lin’s Conjecture via the DecimationHadamard Transform
"... In 1998, Lin presented a conjecture on a class of ternary sequences with ideal 2level autocorrelation in his Ph.D thesis. Those sequences have a very simple structure, i.e., their trace representation has two trace monomial terms. In this paper, we present a proof for the conjecture. The mathemat ..."
Abstract
 Add to MetaCart
(Show Context)
In 1998, Lin presented a conjecture on a class of ternary sequences with ideal 2level autocorrelation in his Ph.D thesis. Those sequences have a very simple structure, i.e., their trace representation has two trace monomial terms. In this paper, we present a proof for the conjecture. The mathematical tools employed are the secondorder multiplexing decimationHadamard transform, Stickelberger’s theorem, the Teichmüller character, and combinatorial techniques for enumerating the Hamming weights of ternary numbers. As a byproduct, we also prove that the Lin conjectured ternary sequences are Hadamard equivalent to ternary msequences. Index Terms. Teichmüller character, decimationHadamard transform, multiplexing decimationHadamard transform, Stickelberger’s theorem, twolevel autocorrelation. 1
GENERALIZED PARY SEQUENCES WITH TWOLEVEL AUTOCORRELATION
"... In this paper, we find a family ofary sequences with ideal twolevel autocorrelation with symbols in the finite field. The proposed family may be considered as a generalization of the wellknown nonbinary sequences introduced by Helleseth and Gong. Using the constructed sequences andsequences, we ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper, we find a family ofary sequences with ideal twolevel autocorrelation with symbols in the finite field. The proposed family may be considered as a generalization of the wellknown nonbinary sequences introduced by Helleseth and Gong. Using the constructed sequences andsequences, we present a family ofary sequences of which the correlation property is optimal in terms of the Welch lower bound.