Bounds on the minimum distance of additive quantum codes

Bounds on [[63,42]]2

lower bound:6
upper bound:7

Construction

Construction type: LiuGuanDuMa

Construction of a [[63,42,6]] quantum code:
[1]:  [[63, 42, 6]] quantum code over GF(2^2)
     cyclic code of length 63 with generating polynomial w*x^62 + w*x^60 + w^2*x^59 + w^2*x^56 + x^55 + w*x^54 + w*x^53 + w*x^52 + w^2*x^51 + w*x^50 + w^2*x^49 + w*x^48 + x^47 + x^45 + x^44 + x^43 + w^2*x^42 + w^2*x^41 + x^40 + w^2*x^39 + w^2*x^38 + w^2*x^37 + w^2*x^36 + w^2*x^35 + w*x^33 + w*x^31 + w^2*x^29 + w*x^28 + w*x^26 + w^2*x^25 + w*x^24 + w^2*x^22 + w^2*x^21 + w*x^20 + x^18 + w*x^15 + w*x^14 + w^2*x^13 + w*x^12 + 1

    stabilizer matrix:

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

last modified: 2024-04-24

Notes


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