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Enlargement of Calderbank-Shor-Steane quantum codes. (English) Zbl 0960.94033
Summary: It is shown that a classical error correcting code $C= [n,k,d]$ which contains its dual, $C^\perp \subseteq C$, and which can be enlarged to $C'= [n, k'> k+1, d']$, can be converted into a quantum code of parameters $[[n, k+k'- n, \min (d, \lceil 3d'/2\rceil)]]$. This is a generalization of a previous construction, it enables many new codes of good efficiency to be discovered. Examples based on classical Bose-Chaudhuri-Hocquenghem (BCH) codes are discussed.

94B60Other types of codes
81P68Quantum computation
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