The appellate review of records of trial provided by this code, the proceedings, findings and sentences of court-martial as reviewed and approved, as required by this code, and all dismissals and discharges carried into execution under sentences by court-martial following review and approval as required by this code, are final and conclusive. Orders publishing the proceedings of the court-martial and all action taken pursuant to those proceedings are binding upon all departments, courts, agencies and officers of the state, subject only to action upon a petition for a new trial as provided in Section 33-13-425.