Computer Science ›› 2015, Vol. 42 ›› Issue (9): 144-146.doi: 10.11896/j.issn.1002-137X.2015.09.027

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Distribution of a Family of Five-valued Cross Correlation Function

XU Li-ping and HU Bin   

  • Online:2018-11-14 Published:2018-11-14

Abstract: Fewvalued cross correlation functions of msequences always interest the researchers.Multivariateequation of higher degree over finite field becomes the key to determine this problem.Most studies ofcross correlation functions when decimated factor is the form of d=(pl+1)/(pk+1) are based on binary msequences(p=2).The paper took pary msequences into account when l=2k.Using the theory of quadratic form,we proved that their cross correlation function is fivevalued.Taking association scheme into consideration,we transformed the problem of cross correlation distribution to the study of the ranks of quadratic form.Finally the complete fivevalued cross correlation distribution of pary msequences was determined.

Key words: msequences,Cross correlation function,Correlation distribution,Quadratic form,Association scheme

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