  The Reed-Muller codes are a family of error-correcting codes that have been
widely studied in coding theory. In 2020, Wei Yan and Sian-Jheng Lin introduced
a variant of Reed-Muller codes so called symmetric Reed-Muller codes. We
investigate linear maps of the automorphism group of symmetric Reed-Muller
codes and show that the set of these linear maps forms a subgroup of the
general linear group, which is the automorphism group of punctured Reed-Muller
codes. We provide a method to determine all the automorphisms in this subgroup
explicitly for some special cases.
