Codes and the Steenrod algebra

Year 2017, Volume: 4 Issue: 2 (Special Issue: Noncommutative rings and their applications), 141 - 154, 10.01.2017

Steven T. Dougherty Tane Vergili

https://doi.org/10.13069/jacodesmath.284950

Cited By: 1

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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