Quantum error correcting codes for specific position errors, which are a different type from ordinary quantum error correcting codes, are proposed. The quantum Hamming bound is modified to apply to such codes. Furthermore, an example of the code which breaks the modified quantum Hamming bound is shown.
I develop methods for analyzing quantum error-correcting codes, and use these methods to construct an infinite class of codes saturating the quantum Hamming bound. These codes encode k=n-j-2 quantum bits (qubits) in n=2j qubits and correct t=1 error. \textcopyright{} 1996 The American Physical Society.