The cross-correlation between an m-sequence of period p^n-1 and its d-decimated sequence with d=(p^n-1)/3 + p^i is shown to take exactly 13 distinct values when p≡1 mod 3 and the given modular condition holds.
The number of solutions of cubic diagonal equations over finite fields,
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Sequences with thirteen-valued cross correlations
The cross-correlation between an m-sequence of period p^n-1 and its d-decimated sequence with d=(p^n-1)/3 + p^i is shown to take exactly 13 distinct values when p≡1 mod 3 and the given modular condition holds.