Journal
DESIGNS CODES AND CRYPTOGRAPHY
Volume 73, Issue 2, Pages 417-424Publisher
SPRINGER
DOI: 10.1007/s10623-014-9934-8
Keywords
Quantum error-correcting code; Linear code; Construction X
Funding
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Collaborative Research Group Mathematics of Quantum Information of the Pacific Institute for the Mathematical Sciences (PIMS)
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Construction X and its variants are known from the theory of classical error control codes. We present instances of these constructions that produce binary stabilizer quantum error control codes from arbitrary quaternary linear codes. Our construction does not require the classical linear code that is used as the ingredient to satisfy the dual containment condition, or, equivalently, is not required to satisfy the self-orthogonality condition. We prove lower bounds on the minimum distance of quantum codes obtained from our construction. We give examples of record breaking quantum codes produced from our construction. In these examples, the ingredient code is nearly dual containing, or, equivalently, is nearly self-orthogonal, by which we mean that is positive but small.
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