Some results on a group under which symmetric reed-muller codes are invariant

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