Bounds on the minimum distance of additive quantum codes

Bounds on [[88,47]]2

lower bound:8
upper bound:14

Construction

Construction of a [[88,47,8]] quantum code:
[1]:  [[85, 49, 8]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomial w^2*x^83 + x^82 + x^79 + w^2*x^76 + w*x^75 + w^2*x^74 + w^2*x^73 + w*x^71 + w*x^70 + x^69 + w^2*x^68 + w*x^67 + x^66 + w^2*x^64 + w^2*x^63 + w*x^62 + w*x^61 + w^2*x^59 + x^58 + x^57 + w^2*x^56 + w*x^55 + x^54 + x^52 + w^2*x^50 + w^2*x^49 + x^48 + x^45 + x^44 + w*x^42 + w^2*x^41 + w*x^35 + w^2*x^34 + w^2*x^33 + w*x^31 + x^30 + w^2*x^29 + x^27 + x^26 + x^24 + x^23 + w^2*x^22 + x^20 + x^19 + x^18 + 1
[2]:  [[85, 47, 8]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[88, 47, 8]] quantum code over GF(2^2)
     ExtendCode [2] by 3

    stabilizer matrix:

      [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 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 0|0 1 1 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0|0 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0|0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 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 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 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0|1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 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 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0|0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0|1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 1 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 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0|0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0|0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0|1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 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 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 0|0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0|1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0|1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 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 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0|0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0|1 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0|1 0 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 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 1 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 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 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 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0|0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 0 1 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 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 1 0 0 0 1 1 1 1 0 0 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 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 1 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0]
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      [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 1 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0|0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0]
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      [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 1 0 0 1 1 1 1 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0|1 1 1 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0|0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0|0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0]
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last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014