Abstract
Quantum codes are fundamental to the error protection in quantum computers. Several families of good or optimal quantum codes were constructed by several researches over time [4, 17, 25, 27, 28, 30, 39, 45, 46, 54, 55, 62, 72–74, 77–81, 89, 91, 105, 106, 111, 138, 147, 148, 162, 165]. The Calderbank–Shor–Steane (CSS) construction is a remarkable technique to construct quantum codes derived from classical ones. As was said previously, such technique has been applied by a great number of quantum coding researchers in order to derive efficient quantum codes. With the possible advent of efficient quantum computers, it is extremely important to investigate how to obtain families of efficient quantum codes. Based on these facts, we present here some constructions of quantum codes derived from several classes of classical codes by means of the CSS construction. The classical codes utilized here are the well-known Bose–Chaudhuri–Hocquenghem (BCH) (Sects. 5.1, 5.2, 5.3), algebraic geometry codes (Sect. 5.4) and quantum synchronizable codes (Sect. 5.5).
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