Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published January 1999 | Submitted + Published
Journal Article Open

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 1 is unique (implying that the well-known one-qubit-in-five single-error 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.

Additional Information

© 1999 IEEE. Manuscript received May 26, 1997; revised March 4, 1998. The author would like to thank A. R. Calderbank, P. Shor, and N. Sloane for many helpful conversations, as well as the anonymous referees for helpful comments.

Attached Files

Published - 00746807.pdf

Submitted - 9704043.pdf

Files

9704043.pdf
Files (403.8 kB)
Name Size Download all
md5:3be1a0578c30ab649dcc8ef224d6d8cf
164.4 kB Preview Download
md5:1b5bb139891b1a4961e17d6e06eb4f82
239.4 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
March 5, 2024