A Characterization of Weight-Preserving Automorphisms of Group Algebras
Robert Miller · Journal of Information and Optimization Sciences · 2013
In this paper we characterize all weight-preserving automorphisms of a group algebra. Examples of such automorphisms over F2 have been studied by MacWilliams in the case of cyclic-group algebras (cyclic codes), and later by Miller in the case of abelian-group algebras (abelian codes). In the binary case, we show that every weight-preserving automorphism of F2 [G] arises by extending an automorphism of G to F2 [G] by linearity.