Correlation of binary sequence families derived from the multiplicative characters of finite fields

Zilong Wang; Guang Gong

doi:10.3934/amc.2013.7.475

Article Contents

2013, Volume 7, Issue 4: 475-484. Doi: 10.3934/amc.2013.7.475

This issue Previous Article ($\sigma,\delta$)-codes Next Article Empirical optimization of divisor arithmetic on hyperelliptic curves over $\mathbb{F}_{2^m}$

Correlation of binary sequence families derived from the multiplicative characters of finite fields

Zilong Wang^1, and
Guang Gong^2,

1.
State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, Shanxi 710071
2.
Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1

Received: November 2012

Published: November 2013

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Abstract

In this paper, new constructions of the binary sequence families of period $q-1$ with large family size and low correlation, derived from multiplicative characters of finite fields for odd prime powers, are proposed. For $m ≥ 2$, the maximum correlation magnitudes of new sequence families $\mathcal{S}_m$ are bounded by $(2m-2)\sqrt{q}+2m+2$, and the family sizes of $\mathcal{S}_m$ are given by $q-1$ for $m=2$, $2(q-1)-1$ for $m=3$, $(q^2-1)q^{\frac{m-4}{2}}$ for $m$ even, $m>2$, and $2(q-1)q^{\frac{m-3}{2}}$ for $m$ odd, $m>3$. It is shown that the known binary Sidel'nikov-based sequence families are equivalent to the new constructions for the case $m=2$.

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Mathematics Subject Classification: Primary: 94B25, 11T24.

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