Can a long-term sexual offender registration challenge be brought in a petition for writ of habeas corpus or writ of mandate?

petition for writ of habeas corpus or a petition for writ of mandate. (Cf. People v. Picklesimer (2010) 48 Cal.4th 330, 337-340 [holding that constitutional challenge to sex offender registration requirement could not be brought in "long-since-final" criminal case, and must instead be brought in a petition for writ of mandate because " '[t]here is no statutory authority for a trial court to entertain a postjudgment motion that is unrelated to any proceeding then pending before the court' "].)