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Ternary m-sequences with three-valued cross-correlation function: new decimations of Welch and Niho type

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4 Author(s)
Dobbertin, H. ; Inst. fur Math., Klagenfurt Univ., Austria ; Helleseth, T. ; Kumar, P.V. ; Martinsen, H.

We show that the cross correlation between two ternary m-sequences of period 3n-1 that differ by the decimation d=2·3m+1, where n=2m+1, takes on three different values. We conjecture the same result for the decimation d=2·3 r+1, where n is odd and r is defined by the condition 4r+1≡0 mod n. These two new cases form in a sense ternary counterparts of two previously confirmed binary cases, the conjectures of Welch and Niho (1972)

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Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 4 )