Further results on product codes

A new class of codes, called product generator codes, which are similar to Elias's iterated codes, are investigated. An important subclass of these codes is the generalized Reed-Muller codes. If the original codes that are iterated to produce a product code are
L_1
and
L_2
-step orthogonalizable, then the product code is (
L_1 + L_2 - 1
)-step orthogonalizable. Further if a
\nu
th-order product generator code is produced from these original
L
-step orthogonal izable codes, the new code is at most
(\nu +1)
step orthogonalizable.