## Bounds on the minimum distance of additive quantum codes

### Bounds on [[35,32]]_{2}

lower bound: | 2 |

upper bound: | 2 |

### Construction

Construction of a [[35,32,2]] quantum code:
[1]: [[34, 32, 2]] quantum code over GF(2^2)
Distance two code
[2]: [[35, 32, 2]] quantum code over GF(2^2)
ExtendCode [1] by 1
stabilizer matrix:
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
last modified: 2005-06-29

### Notes

- All codes establishing the lower bounds where constructed using MAGMA.
- Most upper bounds on qubit codes for
*n≤100* are based on a MAGMA program by Eric Rains.
- For
*n>100*, the upper bounds on qubit codes are weak (and not necessarily monotone in *k*).
- Some additional information can be found in the book by Nebe, Rains, and Sloane.
- My apologies to all authors that have contributed codes to this table for not giving specific credits.

This page is maintained by
Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024