Monomial automorphisms of the linear and simple components of the Hamming code

The linear and simple components of the Hamming code are the spans of the codewords having weight 3 and unit in the given coordinate position over the finite field $\mathbb{F}_q$ and its prime subfield $\mathbb{F}_p$ respectively. The monomial automorphism groups of such components are described. The order of the monomial automorphism group of a linear component is obtained. Bibl. 21.