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东北数学：英文版

A New Description of the Additive Quantum Codes

Liu Huan-ping

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

A new description of the additive quantum codes is presented and a new way to construct good quantum codes [[n,k,d]] is given by using classical binary codes with specific properties in F23n. We show several consequences and examples of good quantum codes by using our new description of the additive quantum codes.

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There have been various constructions of classical codes from polynomial valuations in literature [2], [7], [8], [10], [11]. In this paper, we present a construction of classical codes based on polynomial construction again. One of the features of this construction is that not only the classical codes arisen from the construction have good parameters, but also quantum codes with reasonably good parameters can be produced from these classical codes. In particular, some new quantum codes are constructed (see Examples V.5 and V.6).
The stabilizer method for constructing a class of asymmetric quantum codes (AQC), called additive AQC, has been established by Aly et.al. In this paper, we present a new characterization of AQC, which generalizes a result of the symmetric case known previously. As an application of the characterization, we establish a relationship of AQC with classical error-correcting codes and show a few examples of good AQC with specific parameters. By using this relationship, we obtain an asymptotic bound on AQCs from algebraic geometry codes.
Nonadditive Quantum Codes from Z4\Z_4Z4​-Codes
Non additive binary quantum codes are constructed by using classical Z4\Z_4Z4​-linear binary codes.