Abstract
The theory of quantum error-correcting codes has been extended to asymmetric quantum channels-qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in constructing quantum error-correcting codes has focused on code constructions for symmetric quantum channels. Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting (AEAQEC) code, and gave a Gilbert–Varshamov bound for AEAQEC codes. Then they present the explicit computation of the parameters of AEAQEC codes coming from BCH codes. In this paper, we first establish a bound for pure AEAQEC codes similar to the quantum Singleton bound, and introduce the definition of pure AEAQEC MDS codes. Then we construct three new families of AQEAEC codes by means of Vandermonde matrices, extended GRS codes and cyclic codes. The AEQAEC codes here have better parameters than the ones available in the literature.
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