Dergiler / Journal of Algebra Combinatorics Discrete Structures and Applications / 2017 / Cilt: 4 - Sayı: 2 (Special Issue: Noncommutative rings and their applications) #90795

Codes and the Steenrod algebra

Steven T. DOUGHERTY, Tane VERGİLİ

Dergi: Journal of Algebra Combinatorics Discrete Structures and Applications
Sayı: 2017 · Cilt: 4 - Sayı: 2 (Special Issue: Noncommutative rings and their applications) #90795
Sayfa: 141–154
DOI: —

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.