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The number of cross-join pairs in maximum length linear sequences

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2 Author(s)
Helleseth, T. ; Dept. of Inf., Bergen Univ., Norway ; Klove, T.

It has been conjectured by T. Chang et al. (1990) that the number of cross-join pairs in a maximum length linear sequence equals (2n-1-1)(2n-1-2)/6. A maximum length linear sequence (an m-sequence) of length 2n-1 is a binary sequence which satisfies a linear recurrence whose characteristic polynomial is primitive of degree n. The number of primitive polynomials is given by φ(2n-1)/n, where φ is Euler's φ-function. A proof of the conjecture is given

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Information Theory, IEEE Transactions on  (Volume:37 ,  Issue: 6 )