Bounds on the minimum distance of additive quantum codes

Bounds on [[30,7]]2

lower bound:7
upper bound:9

Construction

Construction of a [[30,7,7]] quantum code:
[1]:  [[30, 8, 7]] Quantum code over GF(2^2)
     cyclic code of length 30 with generating polynomial x^29 + x^28 + w*x^27 + x^26 + w^2*x^24 + x^23 + w*x^22 + x^20 + x^18 + w^2*x^17 + w*x^16 + w*x^15 + x^14 + w^2*x^13 + 1
[2]:  [[30, 7, 7]] Quantum code over GF(2^2)
     Subcode of [1]

    stabilizer matrix:

      [1 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 1 0|1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 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 1 1|0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 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 1 0 1 0 0 0 1 0|0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1]
      [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 1 0 0 1 1|1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0|1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1]
      [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 1 0 1 1 1|1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0]
      [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0|0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 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 1 0 1 1 0|0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0|0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 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 1 0 1 0 1|0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0|1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1]
      [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 1 1 0|1 1 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0|0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 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 1 0 0 0 1|0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0|1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1]
      [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 1 1 1|1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 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 1 0 1 0 0 0 0 0|0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1]
      [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 1 0 0 1 0|1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0|0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1]
      [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 1 0 1 0 0|1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1]
      [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 1 0 1 0|1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 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 1 0 1|0 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 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 1 0 0 0 0 1 0|0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1]

last modified: 2005-06-27

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014