Codes and the Steenrod algebra

Abstract

We study codes over the finite sub Hopf algebras of the Steenrod algebra. We define three dualities for codes over these rings, namely the Eulidean duality, the Hermitian duality and a duality based on the underlying additive group structure. We study self-dual codes, namely codes equal to their orthogonal, with respect to all three dualities.

Keywords

• Self-dual codes,Non-commutative rings,Steenrod algebra

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