New Sets of Binary and Ternary Sequences with Low Correlation

  title={New Sets of Binary and Ternary Sequences with Low Correlation},
  author={Evgeny I. Krengel and Andrew Z. Tirkel and Thomas E. Hall},
New binary and ternary sequences with low correlation and simple implementation are presented. The sequences are unfolded from arrays, whose columns are cyclic shifts of a short sequence or constant columns and whose shift sequence (sequence of column shifts) has the distinct difference property. It is known that a binary m-sequence/GMW sequence of length 2$^{\rm 2{\it m}}$ – 1 can be folded row-by-row into an array of 2m – 1 rows of length 2m + 1. We use this to construct new arrays which have… 

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

  • Jin-Song WangWenfeng Qi
  • Computer Science
    2007 3rd International Workshop on Signal Design and Its Applications in Communications
  • 2007
The correlation property of the proposed sequence family is a little weak towards Welch bound, however, the linear complexity of each sequence is high, some of which can even reach p(p + 2).

Matrix construction using cyclic shifts of a column

  • A. TirkelT. Hall
  • Computer Science
    Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.
  • 2005
The synthesis of matrices with good correlation, from cyclic shifts of pseudonoise columns, from shift sequences of m-arrays to produce arrays for watermarking of digital images is described.

Arrays composed from the extended rational cycle

A unified method of obtaining multivariate recursion polynomials and their footprints for all finite multidimensional arrays and shows that the size of the footprint is invariant under dimensional transformations based on the Chinese Remainder Theorem.

Sequence Sets in Wireless Communication Systems: A Survey

The properties of orthogonal sequences and their relationships that make them attractive to be used in communication systems are described and some ideas to motivate research to improve those properties are offered.



A new class of spreading sequences

  • A. TirkelT. HallC. F. Osborne
  • Mathematics
    1988 IEEE 5th International Symposium on Spread Spectrum Techniques and Applications - Proceedings. Spread Technology to Africa (Cat. No.98TH8333)
  • 1998
The resulting sequences form a family comparable in size and figure of merit to that of Gold codes, but available in many different (composite) lengths, and possess enhanced immunity against cryptographic attack, owing to their large linear and nonlinear span.

New designs for signal sets with low cross correlation, balance property, and largelinear span: GF(p) case

  • G. Gong
  • Computer Science
    IEEE Trans. Inf. Theory
  • 2002
New designs for families of sequences over GF(p) with low cross correlation, balance property, and large linear span are presented and it is shown that some families of these sequences can be implemented efficiently in both hardware and software.

Binary Pseudorandom Sequences of Period 2n-1 with Ideal Autocorrelation

Five new classes of binary sequences of period 2/sup n/-1 with ideal autocorrelation, which correspond to new cyclic Hadamard difference sets, were found by extensive computer search.

Crosscorrelation of M-sequences and GMW-sequences with the same primitive polynomial

  • R. Games
  • Computer Science
    Discret. Appl. Math.
  • 1985

Families of Matrices with Good Auto and Cross-Correlation

A family of p-1 square p% p matrices whose periodic cross-correlation values are uniformly –p,0,+p is constructed, which has resulted in the superimposed embedding of twelve of the matrices in the standard image “Lenna” and their subs equent retrieval without recourse to the unmarked image.

On the Linear Complexity of Legendre Sequences

We determine the linear complexity of all Legendre sequences and the (monic) feedback polynomial of the shortest linear feedback shift register that generates such a Legendre sequence. The result

On the linear complexity of Hall's sextic residue sequences

In this correspondence, the characteristic polynomial and hence the linear complexity of Hall's sextic residue sequences are determined.

Number Theory in Science and Communication

な 応用,第 3 部合同, 第 4 部暗号と除数 , 第 5 部剰余 と 回折 , 第 6 部中国 人 の , 及 び他の 高速 ア ル ゴ リズ ム ,第 MR . Schreeder 著 (Springer, ベ ル リ ン,ハ イデ ル ベ ル ク,1984,324頁) 7 部擬似素数,メ ー ビ ウ ス 変 換,及び分割,第 8部 円 周等分割と多項式, 第 9部ガ ロ ア

Signal Design for Ultra-wideband Radio

A variety of sequence design problems, motivated by UWB system constraints, will be presented, and design for time-hopping, for spectral flatness, for rapid acquisition, and for multiple access will be discussed.

Cyclic Difference Sets

Existence questions.- Multipliers and constructive existence tests.- Difference sets of special type.- Families of difference sets.- Miscellany.