Abstract
In this letter, a method of constructing Hermitian dual containing quaternary linear codes from general quaternary linear codes is proposed. Based on this result, a construction method of binary linear quantum codes is obtained. Using three cyclic codes and one linear code over $\mathbb {F}_{4}$ that are not Hermitian dual containing, we construct four record breaking binary linear quantum codes. Furthermore, ten new record breaking binary additive quantum codes are derived from these four linear quantum codes by propagation rule.
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