Special Issue on Recent Advances in Coding Theory and Cryptography In honor of Joachim Rosenthal
Guest Editors: Elisa Gorla, Anna-Lena Horlemann, Roxana Smarandache and Jens Zumbrägel

Abstract

We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric quantum codes. We set up the theoretic framework for this weight and metric, including upper and lower bounds, asymptotic behavior of random codes, and we show the existence of an optimal family of codes achieving the Singleton-type upper bound.

Communicated by Jens Zumbraegel

Keywords:

AMSC: 11T71, 94B05, 94B65

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