Gray code orders for -ary words avoiding a given factor

Based on order relations inspired by the binary reflected Gray code (BRGC) we define Gray codes and give a generating algorithm for -ary words avoiding a prescribed factor. These generalize an early 2001 result and a very recent one published by some of the present authors, and can be seen as an alternative to those of Squire published in 1996. Among the involved tools, we make use of generalized BRGC order relations, ultimate periodicity of infinite words, and word matching techniques.