A mass formula for self-dual permutation codes
Let \(V\) be a right \(A\)-module, where \(A\) is a finite semisimple algebra over a finite field \(\mathbb F\). Assume that \(V\) carries a non-degenerate equivariant form \(\varphi\). In the paper the author gives the total number \(M_{(V,\varphi)}\) of self-dual codes in an \(A\)-module \(V\), provided that there exists at least one such code. The number \(M_{(V,\varphi)}\) is determined via a Morita equivalence. The mass formula relates the ratio \(M_{(V,\varphi)}/|\Gamma|\) to the stabilizer orders of \(\Gamma\)-orbits, where \(\Gamma\) is a subgroup of the weak isometries group \(\text{Aut}_{\text{weak}}(V)\).
scientific article; zbMATH DE number 5603989
scientific article