From the NM PED Website ---> http://www.ped.state.nm.us/HomeSchools/
""Will my child earn credits toward a public high school diploma while home schooling?
No, unless you purchase a high school diploma program (or specific courses) from an accredited correspondence high school. Under this type of setting the child is still considered to be home schooling until completion.
Can I home school my child until he/she is ready for the GED?
Yes. For more information on GED please visit the department's web site at http://www.ped.state.nm.us/AssessmentAccountability/GED/