  The (classical) crosscorrelation is an important measure of pseudorandomness
of two binary sequences for applications in communications. The arithmetic
crosscorrelation is another figure of merit introduced by Goresky and Klapper
generalizing Mandelbaum's arithmetic autocorrelation.
  First we observe that the arithmetic crosscorrelation is constant for two
binary sequences of coprime periods which complements the analogous result for
the classical crosscorrelation.
  Then we prove upper bounds for the constant arithmetic crosscorrelation of
two Legendre sequences of different periods and of two binary $m$-sequences of
coprime periods, respectively.
