Abstract
In quasi-synchronous frequency hopping code division multiple-access systems, low hit zone frequency hopping sequences are commonly employed to minimize multiple-access interferences. In order to evaluate the goodness of low hit zone frequency hopping sequences design, the periodic Hamming correlation is used as an important measure. But aperiodic Hamming correlation of frequency hopping sequences matters in real applications, although it received little attraction in the literatures compared with the periodic Hamming correlation. In this paper, the new lower bounds on aperiodic Hamming correlation of the low hit zone frequency hopping sequences, with respect to the size of the frequency slot set, the sequence length, low hit zone, the family size, the maximum aperiodic Hamming autocorrelation and the maximum aperiodic Hamming crosscorrelation are established. The new bounds are tighter than the previous bounds. Specially, the new bounds include the second powers of the maximum aperiodic Hamming autocorrelation and the maximum aperiodic Hamming crosscorrelation but the previous bounds do not include them.
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This work was supported by National Science Foundation of China (Grant No. 61271244).
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Communicated by C. J. Colbourn.
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Han, H., Peng, D. & Liu, X. New lower bounds on the aperiodic Hamming correlations of frequency hopping sequences with low hit zone. Des. Codes Cryptogr. 75, 157–174 (2015). https://doi.org/10.1007/s10623-013-9900-x
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DOI: https://doi.org/10.1007/s10623-013-9900-x
Keywords
- Frequency hopping sequences
- Aperiodic Hamming correlation
- Low hit zone
- Quasi-synchronous frequency hopping communication
- Multiple-access