Bounds on the minimum distance of additive quantum codes

Bounds on [[91,51]]2

lower bound:8
upper bound:13

Construction

Construction of a [[91,51,8]] quantum code:
[1]:  [[85, 53, 7]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomial w*x^84 + w*x^83 + x^81 + w*x^80 + w^2*x^79 + x^78 + x^77 + w^2*x^76 + x^75 + w^2*x^74 + w^2*x^73 + x^72 + w^2*x^71 + x^70 + w*x^69 + w^2*x^68 + w*x^66 + w^2*x^64 + x^63 + x^62 + x^61 + x^60 + w^2*x^59 + w^2*x^58 + w^2*x^57 + w*x^55 + w^2*x^54 + x^53 + w*x^52 + x^51 + w*x^50 + w*x^49 + x^48 + x^47 + x^45 + x^43 + x^42 + x^41 + w^2*x^39 + w*x^38 + x^37 + w*x^36 + x^35 + x^34 + w*x^33 + w*x^32 + x^30 + w*x^28 + w^2*x^27 + x^26 + w*x^25 + w*x^24 + w^2*x^23 + w*x^22 + x^20 + x^19 + x^18 + w*x^17 + x^16 + 1
[2]:  [[86, 52, 8]] quantum code over GF(2^2)
     standard lengthening of  [1]
[3]:  [[86, 51, 8]] quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[91, 51, 8]] quantum code over GF(2^2)
     ExtendCode [3] by 5

    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 1 0 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0|0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 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 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 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0|0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 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 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0|0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 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 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 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0|0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 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 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0|0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 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 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 0|0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 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 1 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0|0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 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 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0|0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 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 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0|0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 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 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0|0 0 0 1 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 0 0|0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 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 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 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0|0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 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 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0|0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0 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 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 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0|0 1 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 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 0 0 0 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0|0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 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 1 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 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 0 1 0 1 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 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 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 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 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0|0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 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 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 1 1 1 1 1 1 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 1 0 1 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0|0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 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 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 1 0 1 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0|0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 1 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0|0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 0|0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 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 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 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0|0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 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 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0|0 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0 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 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 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0|0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 0 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