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Jonathan Jedwab - One of the best experts on this subject based on the ideXlab platform.
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Advances in the merit factor problem for Binary Sequences
Journal of Combinatorial Theory Series A, 2013Co-Authors: Jonathan Jedwab, Daniel J. Katz, Kai-uwe SchmidtAbstract:The identification of Binary Sequences with large merit factor (small mean-squared aperiodic autocorrelation) is an old problem of complex analysis and combinatorial optimization, with practical importance in digital communications engineering and condensed matter physics. We establish the asymptotic merit factor of several families of Binary Sequences and thereby prove various conjectures, explain numerical evidence presented by other authors, and bring together within a single framework results previously appearing in scattered form. We exhibit, for the first time, families of skew-symmetric Sequences whose asymptotic merit factor is as large as the best known value (an algebraic number greater than 6.34) for all Binary Sequences; this is interesting in light of [email protected]?s conjecture that the subclass of skew-symmetric Sequences has asymptotically optimal merit factor. Our methods combine Fourier analysis, estimation of character sums, and estimation of the number of lattice points in polyhedra.
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Advances in the merit factor problem for Binary Sequences
arXiv: Combinatorics, 2012Co-Authors: Jonathan Jedwab, Daniel J. Katz, Kai-uwe SchmidtAbstract:The identification of Binary Sequences with large merit factor (small mean-squared aperiodic autocorrelation) is an old problem of complex analysis and combinatorial optimization, with practical importance in digital communications engineering and condensed matter physics. We establish the asymptotic merit factor of several families of Binary Sequences and thereby prove various conjectures, explain numerical evidence presented by other authors, and bring together within a single framework results previously appearing in scattered form. We exhibit, for the first time, families of skew-symmetric Sequences whose asymptotic merit factor is as large as the best known value (an algebraic number greater than 6.34) for all Binary Sequences; this is interesting in light of Golay's conjecture that the subclass of skew-symmetric Sequences has asymptotically optimal merit factor. Our methods combine Fourier analysis, estimation of character sums, and estimation of the number of lattice points in polyhedra.
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bounds on the growth rate of the peak sidelobe level of Binary Sequences
Advances in Mathematics of Communications, 2007Co-Authors: Denis Dmitriev, Jonathan JedwabAbstract:The peak sidelobe level (PSL) of a Binary sequence is the largest absolute value of all its nontrivial aperiodic autocorrelations. A classical prob- lem of digital sequence design is to determine how slowly the PSL of a length n Binary sequence can grow, as n becomes large. Moon and Moser showed in 1968 that the growth rate of the PSL of almost all length n Binary Sequences lies between order p nlogn and p n, but since then no theoretical improvement to these bounds has been found. We present the first numerical evidence on the tightness of these bounds, showing that the PSL of almost all Binary Sequences of length n appears to grow exactly like order p nlogn, and that the PSL of almost all m-Sequences of length n appears to grow exactly like order p n. In the case of m-Sequences, a key algorithmic insight reveals behaviour that was previously well beyond the range of computation.
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the peak sidelobe level of families of Binary Sequences
International Symposium on Information Theory, 2006Co-Authors: Jonathan Jedwab, Kayo YoshidaAbstract:A numerical investigation is presented for the peak sidelobe level (PSL) of Legendre Sequences and maximal length shift register Sequences (m-Sequences). The PSL gives an alternative to the merit factor for measuring the collective smallness of the aperiodic autocorrelations of a Binary sequence. The growth of the PSL of these infinite families of Binary Sequences is tested against the desired growth rate o(radic(n ln n)) for sequence length n. The claim that the PSL of m-Sequences grows like O(radicn), which appears frequently in the radar literature, is concluded to be unproven and not currently supported by data. Notable similarities are uncovered between the PSL and merit factor behaviour under cyclic rotations of the Sequences
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the peak sidelobe level of families of Binary Sequences
IEEE Transactions on Information Theory, 2006Co-Authors: Jonathan Jedwab, Kayo YoshidaAbstract:A numerical investigation is presented for the peak sidelobe level (PSL) of Legendre Sequences, maximal length shift register Sequences (m-Sequences), and Rudin-Shapiro Sequences. The PSL gives an alternative to the merit factor for measuring the collective smallness of the aperiodic autocorrelations of a Binary sequence. The growth of the PSL of these infinite families of Binary Sequences is tested against the desired growth rate o(/spl radic/nlnn) for sequence length n. The claim that the PSL of m-Sequences grows like O(/spl radic/n), which appears frequently in the radar literature, is concluded to be unproven and not currently supported by data. Notable similarities are uncovered between the PSL and merit factor behavior under cyclic rotations of the Sequences.
Keqin Feng - One of the best experts on this subject based on the ideXlab platform.
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on the 2 adic complexity of a class of Binary Sequences of period 4p with optimal autocorrelation magnitude
International Symposium on Information Theory, 2020Co-Authors: Minghui Yang, Lulu Zhang, Keqin FengAbstract:Via interleaving Ding-Helleseth-Lam Sequences, a class of Binary Sequences with optimal autocorrelation magnitude was constructed (Des. Codes and Cryptogr., 2018). Later, Sun et al. determined the upper and lower bounds of the 2-adic complexity of such Sequences (SETA, 2018). In this paper, we determine the exact value of the 2-adic complexity of this class of Sequences. The results show that the 2-adic complexity of this class of Binary Sequences is close to the maximum.
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on the 2 adic complexity of the ding helleseth martinsen Binary Sequences
IEEE Transactions on Information Theory, 2020Co-Authors: Lulu Zhang, Minghui Yang, Jun Zhang, Keqin FengAbstract:We determine the 2-adic complexity of the Ding-Helleseth-Martinsen (DHM) Binary Sequences by using cyclotomic numbers of order four, “Gauss periods” and “quadratic Gauss sums” on finite field $\mathbb {F}_{{q}}$ and valued in $\mathbb {Z}_{2^{{N}}-1}$ , where ${q} \equiv 5\pmod 8$ is a prime number and ${N}=2{q}$ is the period of the DHM Sequences.
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on the 2 adic complexity of a class of Binary Sequences of period 4p with optimal autocorrelation magnitude
arXiv: Information Theory, 2019Co-Authors: Minghui Yang, Lulu Zhang, Keqin FengAbstract:Via interleaving Ding-Helleseth-Lam Sequences, a class of Binary Sequences of period $4p$ with optimal autocorrelation magnitude was constructed in \cite{W. Su}. Later, Fan showed that the linear complexity of this class of Sequences is quite good \cite{C. Fan}. Recently, Sun et al. determined the upper and lower bounds of the 2-adic complexity of such Sequences \cite{Y. Sun3}. We determine the exact value of the 2-adic complexity of this class of Sequences. The results show that the 2-adic complexity of this class of Binary Sequences is close to the maximum.
Cunsheng Ding - One of the best experts on this subject based on the ideXlab platform.
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New Classes of Balanced Quaternary and Almost Balanced Binary Sequences With Optimal Autocorrelation Value
IEEE Transactions on Information Theory, 2010Co-Authors: Xiaohu Tang, Cunsheng DingAbstract:Sequences with optimal autocorrelation property are needed in certain communication systems and cryptography. In this paper, a construction of balanced quaternary Sequences with period N ≡ 2 (mod 4) and optimal autocorrelation value and a construction of almost balanced Binary Sequences with period N ≡ 0 (mod 4) and optimal autocorrelation value are presented. Both constructions are a generalization of earlier ones.
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Binary Sequences with optimal autocorrelation
Theoretical Computer Science, 2009Co-Authors: Ying Cai, Cunsheng DingAbstract:Sequences have important applications in ranging systems, spread spectrum communication systems, multi-terminal system identification, code-division multiple access communication systems, global positioning systems, software testing, circuit testing, computer simulation, and stream ciphers. Sequences and error-correcting codes are also closely related. In this paper, we give a well rounded treatment of Binary Sequences with optimal autocorrelation. We survey known ones and construct new ones.
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new families of Binary Sequences with optimal three level autocorrelation
IEEE Transactions on Information Theory, 2001Co-Authors: Cunsheng Ding, Tor Helleseth, H M MartinsenAbstract:In this correspondence we give several new families of Binary Sequences of period N with optimal three-level autocorrelation, where N/spl equiv/2 (mod 4). These Sequences are either balanced or almost balanced. Our construction is based on cyclotomy.
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Several classes of Binary Sequences with three-level autocorrelation
IEEE Transactions on Information Theory, 1999Co-Authors: Cunsheng Ding, Tor HellesethAbstract:In this correspondence we describe several classes of Binary Sequences with three-level autocorrelation. Those classes of Binary Sequences are based on cyclic almost difference sets. Some classes of Binary Sequences have optimum autocorrelation.
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linear complexity of generalized cyclotomic Binary Sequences of order 2
Finite Fields and Their Applications, 1997Co-Authors: Cunsheng DingAbstract:There are several kinds of cyclotomic Sequences. They have a number of good randomness properties. In this paper we calculate the linear complexity (linear span) of generalized cyclotomic Binary Sequences of order 2. Our results show that their linear complexity is quite good.
Dengguo Feng - One of the best experts on this subject based on the ideXlab platform.
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on the 2 adic complexity and the k error 2 adic complexity of periodic Binary Sequences
IEEE Transactions on Information Theory, 2008Co-Authors: Dengguo FengAbstract:A significant difference between the linear complexity and the 2-adic complexity of periodic Binary Sequences is pointed out in this correspondence. Based on this observation, we present the concept of the symmetric 2-adic complexity of periodic Binary Sequences. The expected value of the 2-adic complexity is determined, and a lower bound on the expected value of the symmetric 2-adic complexity of periodic Binary Sequences is derived. We study the variance of the 2-adic complexity of periodic Binary Sequences, and the exact value for it is given. Because the k-adic complexity of periodic Binary Sequences is unstable, we present the concepts of the kappa-error 2-adic complexity and the k-error symmetric 2-adic complexity, and lower bounds on them are also derived. In particular, we give tighter upper and lower bounds for the minimum k-adic complexity of l-Sequences by substituting two symbols within one period.
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incomplete exponential sums over galois rings with applications to some Binary Sequences derived from z sub 2 sup l
IEEE Transactions on Information Theory, 2006Co-Authors: Dengguo FengAbstract:An upper bound for the incomplete exponential sums over Galois rings is derived explicitly. Based on the incomplete exponential sums, we analyze the partial period properties of some Binary Sequences derived from Z/sub 2//sup l/ in detail, such as the Kerdock-code Binary Sequences and the highest level Sequences of primitive Sequences over Z/sub 2//sup l/. The results show that the partial period distributions and the partial period independent r-pattern distributions of these Binary Sequences are asymptotically uniform. Nontrivial upper bounds for the aperiodic autocorrelation of these Sequences are also given.
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on the 2 adic complexity and the k error 2 adic complexity of periodic Binary Sequences
Lecture Notes in Computer Science, 2005Co-Authors: Dengguo FengAbstract:In this paper, we point out a significant difference between the linear complexity and the 2-adic complexity of periodic Binary Sequences. The concept of the symmetric 2-adic complexity of periodic Binary Sequences is presented based on this observation. We determine the expected value of the 2-adic complexity and derive a lower bound on the expected value of the symmetric 2-adic complexity of periodic Binary Sequences. Because the 2-adic complexity of periodic Binary Sequences is unstable, we present the concepts of the k-error 2-adic complexity and the k-error symmetric 2-adic complexity, and lower bounds on them are also derived.
Xiaohu Tang - One of the best experts on this subject based on the ideXlab platform.
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generic construction of Binary Sequences of period 2n with optimal odd correlation magnitude based on quaternary Sequences of odd period n
IEEE Transactions on Information Theory, 2018Co-Authors: Yang Yang, Xiaohu TangAbstract:Binary Sequences with low odd correlation have important applications in communication systems to reduce interference. In this paper, using the interleaving technique, we present a generic connection between Binary Sequences with low odd correlation and quaternary Sequences with low even correlation. As a result, some new Binary Sequences with optimal odd auto-correlation magnitude are obtained. Besides, two sets consisting of $2^{n}+1$ Binary Sequences of period $2(2^{n}-1)$ with the maximum odd correlation magnitude $2^{((n+1)/ 2)}+2$ are derived, which are the first two optimal classes of Binary sequence sets achieving the Sarwate bound on the odd correlation magnitude in the literature.
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on the linear complexity of Binary Sequences of period 4n with optimal autocorrelation value magnitude
IEEE Transactions on Information Theory, 2011Co-Authors: Xiaohu TangAbstract:Three classes of Binary Sequences of period 4N with optimal autocorrelation value/magnitude have been constructed by Tang and Gong based on interleaving certain kinds of Sequences of period N , i.e., the Legendre sequence, twin-prime sequence and generalized GMW sequence. In this paper, by means of sequence polynomials of the underlying Sequences, the properties of roots of the corresponding sequence polynomials of the interleaved Sequences with period 4N and optimal autocorrelation value/magnitude are discussed in the splitting field of xN-1 . As a consequence, both the minimal polynomials and linear complexities of these three classes of Sequences are completely determined except for the case of the Sequences obtained from the generalized GMW Sequences. For the latter, the minimal polynomial and linear complexity can be specially obtained if the sequence is constructed based on m-Sequences instead of generalized GMW Sequences.
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new constructions of Binary Sequences with optimal autocorrelation value magnitude
IEEE Transactions on Information Theory, 2010Co-Authors: Xiaohu Tang, Guang GongAbstract:In this paper, we give three new constructions of Binary Sequences of period AN with optimal autocorrelation value or optimal autocorrelation magnitude using N × 4 interleaved Sequences. Yu and Gong recently found any Binary sequence of period AN with optimal autocorrelation value constructed from an almost difference set by Arasu et al. is an N × 4 interleaved sequence for which all four columns in its N × 4 array are shift equivalent up to the complement. We found that it is not necessary that four columns are shift equivalent. Instead, it could be a pair of related Sequences together with their shifts as the column Sequences. The first construction is to use a generalized GMW sequence of period N = 2k - 1 and its modified version, the second construction is to use a twin prime sequence of length N = p(p + 2) and its modified version, and the third construction, a pair of Legendre Sequences of period N = p (p odd prime) with their respective first terms complementary (the 2-level autocorrelation property is not needed for the Legendre sequence). The comparison with the known constructions are given. For the new Sequences with optimal autocorrelation value, their corresponding new almost difference sets are also derived.
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New Classes of Balanced Quaternary and Almost Balanced Binary Sequences With Optimal Autocorrelation Value
IEEE Transactions on Information Theory, 2010Co-Authors: Xiaohu Tang, Cunsheng DingAbstract:Sequences with optimal autocorrelation property are needed in certain communication systems and cryptography. In this paper, a construction of balanced quaternary Sequences with period N ≡ 2 (mod 4) and optimal autocorrelation value and a construction of almost balanced Binary Sequences with period N ≡ 0 (mod 4) and optimal autocorrelation value are presented. Both constructions are a generalization of earlier ones.