Asymmetric quantum convolutional codes

TL;DR

This paper introduces the first families of asymmetric quantum convolutional codes constructed algebraically using CSS-type methods, offering diverse parameters and asymmetry suited for quantum error correction.

Contribution

It presents the first algebraic construction of asymmetric quantum convolutional codes with various parameters and types, expanding quantum coding options.

Findings

Constructed the first families of AQCCs using CSS-type methods.

Codes exhibit noncatastrophic generator matrices and significant asymmetry.

Multiple code families with diverse parameters are derived.

Abstract

In this paper, we construct the first families of asymmetric quantum convolutional codes (AQCC)'s. These new AQCC's are constructed by means of the CSS-type construction applied to suitable families of classical convolutional codes, which are also constructed here. The new codes have noncatastrophic generator matrices and they present great asymmetry. Since our constructions are performed algebraically, it is possible to derive several families of such codes and not only codes with specific parameters. Additionally, several different types of such codes are obtained.