Bounds on the minimum distance of additive quantum codes

Bounds on [[80,7]]2

lower bound:15
upper bound:25

Construction

Construction of a [[80,7,15]] quantum code:
[1]:  [[85, 1, 21]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomials [
x^84 + w*x^83 + w^2*x^82 + x^81 + w^2*x^80 + w^2*x^79 + x^78 + w^2*x^77 + w^2*x^76 + w*x^75 + w*x^74 + x^73 + x^72 + w*x^71 + w^2*x^70 + x^69 + w*x^68 + w^2*x^67 + w^2*x^66 + x^65 + w*x^64 + w*x^63 + w^2*x^61 + w^2*x^59 + x^58 + x^55 + w^2*x^53 + w*x^52 + w*x^51 + w*x^50 + w^2*x^48 + w^2*x^47 + x^46 + x^44 + w*x^43 + x^40 + w*x^39 + w^2*x^36 + w^2*x^35 + w^2*x^32 + w*x^31 + x^30 + w^2*x^28 + x^23 + w^2*x^22 + x^21 + w^2*x^19 + x^16 + w*x^15 + w*x^14 + w^2*x^12 + w*x^11 + w^2*x^10 + w*x^8 + w*x^7 + x^6 + w^2*x^5 + w^2*x^3 + w^2*x^2 + x,
x^83 + w^2*x^82 + x^81 + w*x^80 + w*x^79 + x^78 + w^2*x^76 + w^2*x^75 + w*x^74 + x^73 + w^2*x^72 + w*x^71 + w*x^69 + x^68 + w*x^65 + x^64 + w*x^62 + x^61 + w*x^60 + x^59 + w*x^58 + x^57 + w^2*x^56 + x^55 + w*x^52 + w*x^51 + w*x^49 + x^48 + x^47 + w^2*x^46 + w^2*x^45 + x^44 + w^2*x^43 + w*x^42 + w^2*x^41 + w^2*x^40 + x^39 + w*x^37 + w^2*x^35 + w^2*x^34 + w^2*x^33 + w^2*x^32 + x^30 + w^2*x^29 + x^28 + x^27 + x^26 + w*x^25 + w*x^23 + x^22 + x^21 + w*x^20 + x^18 + w*x^17 + w^2*x^16 + w*x^15 + x^13 + w*x^12 + w*x^11 + x^9 + w^2*x^8 + w^2*x^7 + x^6 + x^5 + w*x^4 + w^2*x^3 + w^2*x^2 + x
]
[2]:  [[79, 7, 15]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 80, 81, 82, 83, 84, 85 }
[3]:  [[80, 7, 15]] quantum code over GF(2^2)
     ExtendCode [2] by 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 0 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 0 1 1 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 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 1 0 1 0 0 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 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 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 1 0 1 0 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 0 0 1 0 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 1 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 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 1 1 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 1 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 1 1 1 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 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 1 1 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 1 1 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 1 1 1 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0]
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      [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 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 1 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 1 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 0 0 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 1 0 0 0 0 0 1 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 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 0 0 0 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 1 0 0 0 0 0 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 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 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 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 1 0 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 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 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 0|0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 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 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 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 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 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 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 1 1 0 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 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 1 1 1 1 0 1 0 0 0 1 1 0 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 0]
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last modified: 2006-04-04

Notes


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