  We introduce a family of block-additive automatic sequences, that are
obtained by allocating a weight to each couple of digits, and defining the
$n$th term of the sequence as being the total weight of the integer $n$ written
in base $k$. Under an additional difference condition on the weight function,
these sequences can be interpreted as generalised Rudin-Shapiro sequences, and
we prove that they have the same correlations of order 2 as sequences of
symbols chosen uniformly and independently at random. The speed of convergence
is very fast and is independent of the prime factor decomposition of $k$. This
extends recent work of Tahay. The proof relies on direct observations about
base-$k$ representations of integers and combinatorial considerations. We also
provide extensions of our results to higher-dimensional block-additive
sequences.
