Quantum codes via binary codes over symbol-pair metric

Abstract

Stabilizer codes, introduced in \cite{gottesman}, \cite{GF(4)}, have been a prominent example of quantum codes constructed via classical codes. The paper \cite{GF(4)}, introduces the stabilizer formalism for obtaining additive quantum codes of length n from Hermitian self-orthogonal codes of length n over GF(4). In the present work, we present a few stabilizer code constructions considering binary codes over the symbol-pair metric (see \cite{sp}). Specifically, the present work constructs additive quantum codes of length n from certain binary codes of length n considered over the symbol-pair metric. We also present the Modified CSS Construction which is used to obtain quantum codes with parameters $[[15,$ $4,$ $3\leq d\leq7]]$, $[[31,$ $10,$ $5\leq d\leq9]]$, $[[62,$ $20,$ $5\leq d]]$, $[[63,$ $18,$ $7\leq d]]$.<br>