### Abstract

In this paper, we extend the construction by Yu and Gong for families of M-ary sequences of period q-1 from the array structure of an M-ary Sidelnikov sequence of period q^{2}-1 , where q is a prime power and M|q-1. The construction now applies to the cases of using any period q^{d}-1 for 3\leq d < (1/2)(q-(2/{ q+1) and q>27. The proposed construction results in a family of M-ary seqeunces of period q-1 with: 1) the correlation magnitudes, which are upper bounded by (2d-1) q+1 and 2) the asymptotic size of (M-1)q^{d}-1}/d as q increases. We also characterize some subsets of the above of size ∼ (r-1)q^{d}-1}/d but with a tighter upper bound (2d-2)\sqrt {q}+2 on its correlation magnitude. We discuss reducing both time and memory complexities for the practical implementation of such constructions in some special cases. We further give some approximate size of the newly constructed families in general and an exact count when d is a prime power or a product of two distinct primes. The main results of this paper now give more freedom of tradeoff in the design of M-ary sequence family between the family size and the correlation magnitude of the family.

Original language | English |
---|---|

Article number | 6960077 |

Pages (from-to) | 655-670 |

Number of pages | 16 |

Journal | IEEE Transactions on Information Theory |

Volume | 61 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Science Applications
- Library and Information Sciences

### Cite this

*IEEE Transactions on Information Theory*,

*61*(1), 655-670. [6960077]. https://doi.org/10.1109/TIT.2014.2371461

}

*IEEE Transactions on Information Theory*, vol. 61, no. 1, 6960077, pp. 655-670. https://doi.org/10.1109/TIT.2014.2371461

**New M-ary sequence families with low correlation from the array structure of sidelnikov sequences.** / Kim, Young Tae; Kim, Dae San; Song, Hong Yeop.

Research output: Contribution to journal › Article

TY - JOUR

T1 - New M-ary sequence families with low correlation from the array structure of sidelnikov sequences

AU - Kim, Young Tae

AU - Kim, Dae San

AU - Song, Hong Yeop

PY - 2015/1/1

Y1 - 2015/1/1

N2 - In this paper, we extend the construction by Yu and Gong for families of M-ary sequences of period q-1 from the array structure of an M-ary Sidelnikov sequence of period q2-1 , where q is a prime power and M|q-1. The construction now applies to the cases of using any period qd-1 for 3\leq d < (1/2)(q-(2/{ q+1) and q>27. The proposed construction results in a family of M-ary seqeunces of period q-1 with: 1) the correlation magnitudes, which are upper bounded by (2d-1) q+1 and 2) the asymptotic size of (M-1)qd-1}/d as q increases. We also characterize some subsets of the above of size ∼ (r-1)qd-1}/d but with a tighter upper bound (2d-2)\sqrt {q}+2 on its correlation magnitude. We discuss reducing both time and memory complexities for the practical implementation of such constructions in some special cases. We further give some approximate size of the newly constructed families in general and an exact count when d is a prime power or a product of two distinct primes. The main results of this paper now give more freedom of tradeoff in the design of M-ary sequence family between the family size and the correlation magnitude of the family.

AB - In this paper, we extend the construction by Yu and Gong for families of M-ary sequences of period q-1 from the array structure of an M-ary Sidelnikov sequence of period q2-1 , where q is a prime power and M|q-1. The construction now applies to the cases of using any period qd-1 for 3\leq d < (1/2)(q-(2/{ q+1) and q>27. The proposed construction results in a family of M-ary seqeunces of period q-1 with: 1) the correlation magnitudes, which are upper bounded by (2d-1) q+1 and 2) the asymptotic size of (M-1)qd-1}/d as q increases. We also characterize some subsets of the above of size ∼ (r-1)qd-1}/d but with a tighter upper bound (2d-2)\sqrt {q}+2 on its correlation magnitude. We discuss reducing both time and memory complexities for the practical implementation of such constructions in some special cases. We further give some approximate size of the newly constructed families in general and an exact count when d is a prime power or a product of two distinct primes. The main results of this paper now give more freedom of tradeoff in the design of M-ary sequence family between the family size and the correlation magnitude of the family.

UR - http://www.scopus.com/inward/record.url?scp=84920129922&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920129922&partnerID=8YFLogxK

U2 - 10.1109/TIT.2014.2371461

DO - 10.1109/TIT.2014.2371461

M3 - Article

AN - SCOPUS:84920129922

VL - 61

SP - 655

EP - 670

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 1

M1 - 6960077

ER -