Automorphisms of principal nilpotent self-dual codes in certain modular algebras (Q1073774)

Codes which are principal, nilpotent and self dual in the group algebra \[ A=\mathbb F_ q[X_ 1,\ldots,X_ n]/(X_ 1^{2\ell_ 1}- 1,\ldots,X^{2\ell_ n}-1) \] where \(q=2^ r\) and \(\ell_ i\) is odd, \(1\leq i\leq n\), are investigated. In the first part of the paper some basic results on the algebra \(A\) are reviewed. In particular \(A\) is the direct sum of algebras \(A_ k\), \(1\leq k\leq N\), generated by an idempotent \(e_ k\) and these algebras mutually annihilate. The second part of the paper gives a characterization of principal, nilpotent self-dual codes and shows that all such codes are isomorphic. The final part of the paper constructs polynomials in \(A\) which yield code automorphisms.