Optimal and perfect difference systems of sets from <Emphasis Type="Italic">q</Emphasis>-ary sequences with difference-balanced property |
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Authors: | Zhengchun Zhou Xiaohu Tang |
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Institution: | 1.School of Mathematics,Southwest Jiaotong University,Chengdu,China;2.Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications,Southwest Jiaotong University,Chengdu,China |
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Abstract: | Difference systems of sets (DSS) are important for the construction of codes for synchronization. In this paper, a general
construction of optimal and perfect difference systems of sets based on q-ary sequences of period n = −1 (mod q) with difference- balanced property is presented, where q is a prime power. This works for all the known q-ary sequences with ideal autocorrelation, and generalizes the earlier construction based on ternary sequences with ideal
autocorrelation. In addition, we construct another class of optimal and perfect difference systems of sets, employing decimation
of q-ary d-form sequences of period q
m
−1 with difference-balanced property, which generalizes the previous construction from power functions. |
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Keywords: | |
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