  A new recursive construction of $N$-ary error-correcting output code (ECOC)
matrices for ensemble classification methods is presented, generalizing the
classic doubling construction for binary Hadamard matrices. Given any prime
integer $N$, this deterministic construction generates base-$N$ symmetric
square matrices $M$ of prime-power dimension having optimal minimum Hamming
distance between any two of its rows and columns. Experimental results for six
datasets demonstrate that using these deterministic coding matrices for $N$-ary
ECOC classification yields comparable and in many cases higher accuracy
compared to using randomly generated coding matrices. This is particular true
when $N$ is adaptively chosen so that the dimension of $M$ matches closely with
the number of classes in a dataset, which reduces the loss in minimum Hamming
distance when $M$ is truncated to fit the dataset. This is verified through a
distance formula for $M$ which shows that these adaptive matrices have
significantly higher minimum Hamming distance in comparison to randomly
generated ones.
