Bounds on the minimum distance of additive quantum codes

Bounds on [[35,21]]2

lower bound:4
upper bound:5

Construction

Construction of a [[35,21,4]] quantum code:
[1]:  [[31, 21, 4]] Quantum code over GF(2^2)
     cyclic code of length 31 with generating polynomial x^30 + x^29 + w*x^26 + w^2*x^25 + w^2*x^24 + w^2*x^23 + x^21 + w*x^20 + w*x^18 + w^2*x^17 + x^16 + w*x^15 + x^14 + w*x^13 + x^11 + w^2*x^10 + x^9 + x^8 + w^2*x^7 + x^6 + w*x^5 + 1
[2]:  [[32, 21, 4]] Quantum code over GF(2^2)
     ExtendCode [1] by 1
[3]:  [[35, 21, 4]] Quantum code over GF(2^2)
     ExtendCode [2] by 3

    stabilizer matrix:

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


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