  The Pearson distance has been advocated for improving the error performance
of noisy channels with unknown gain and offset. The Pearson distance can only
fruitfully be used for sets of $q$-ary codewords, called Pearson codes, that
satisfy specific properties. We will analyze constructions and properties of
optimal Pearson codes. We will compare the redundancy of optimal Pearson codes
with the redundancy of prior art $T$-constrained codes, which consist of
$q$-ary sequences in which $T$ pre-determined reference symbols appear at least
once. In particular, it will be shown that for $q\le 3$ the $2$-constrained
codes are optimal Pearson codes, while for $q\ge 4$ these codes are not
optimal.
