Title: Anti-isomorphisms, character modules and self-dual codes over non-commutative rings

Authors: Jay A. Wood

Addresses: Department of Mathematics, Western Michigan University, 1903 W. Michigan Avenue, Kalamazoo, MI 49008–5248, USA

Abstract: This paper is dedicated to Vera Pless. It is an elaboration on ideas of Nebe, Rains and Sloane: by assuming the existence of an anti-isomorphism on a finite ring and by assuming a module alphabet has a well-behaved duality, one is able to study self-dual codes defined over alphabets that are modules over a non-commutative ring. Various examples are discussed.

Keywords: anti-isomorphisms; bi-additive forms; character modules; dual codes; MacWilliams identities; skew-polynomial rings; group rings; Steenrod algebra; self-dual codes; Vera Pless; non-commutative rings.

DOI: 10.1504/IJICOT.2010.032867

International Journal of Information and Coding Theory, 2010 Vol.1 No.4, pp.429 - 444

Published online: 25 Apr 2010 *

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