Quantum codes of minimum distance two
Abstract
It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With this in mind, we present a number of results on codes of minimum distance 2. We first compute the linear programming bound on the dimension of such a code, then show that this bound can only be attained when the code either is of even length, or is of length 3 or 5. We next consider questions of uniqueness, showing that the optimal code of length 2 or 4 is unique (implying that the wellknown onequbitinfive singleerror correcting code is unique), and presenting nonadditive optimal codes of all greater even lengths. Finally, we compute the full automorphism group of the more important distance 2 codes, allowing us to determine the full automorphism group of any GF(4)linear code.
 Publication:

arXiv eprints
 Pub Date:
 April 1997
 DOI:
 10.48550/arXiv.quantph/9704043
 arXiv:
 arXiv:quantph/9704043
 Bibcode:
 1997quant.ph..4043R
 Keywords:

 Quantum Physics
 EPrint:
 13 pages, AMSTeX