Is it permissible for a woman to write Quranic surahs in Arabic during menstruation?

A menstruating woman and a woman in post-natal bleeding are permitted to recite the Quran without touching the Mushaf (the physical copy of the Quran). They are also allowed to write verses from it, provided they do not touch the letters of the Mushaf. Furthermore, some scholars have permitted touching a tablet on which verses are written, provided the touch is on an empty space without writing.