Bounds on the minimum distance of additive quantum codes

Bounds on [[87,62]]2

lower bound:6
upper bound:8

Construction

Construction of a [[87,62,6]] quantum code:
[1]:  [[85, 65, 5]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomial x^84 + w^2*x^83 + x^82 + x^81 + x^80 + w^2*x^78 + w^2*x^77 + x^76 + w^2*x^75 + w^2*x^73 + w*x^72 + w^2*x^71 + w*x^69 + w^2*x^68 + w*x^65 + x^64 + x^63 + x^62 + w^2*x^61 + w*x^60 + w*x^59 + x^58 + w*x^57 + w^2*x^56 + w^2*x^55 + x^53 + x^52 + w^2*x^51 + x^49 + w*x^48 + w*x^47 + w*x^46 + x^45 + x^44 + x^43 + x^42 + w*x^41 + w^2*x^40 + x^38 + x^37 + x^34 + w^2*x^33 + w^2*x^32 + w*x^31 + x^30 + w^2*x^29 + w*x^28 + x^27 + w*x^26 + x^25 + x^24 + x^23 + w*x^22 + w*x^20 + w^2*x^19 + w^2*x^18 + x^17 + x^16 + w^2*x^15 + w*x^14 + x^13 + x^12 + x^10 + 1
[2]:  [[86, 64, 6]] quantum code over GF(2^2)
     standard lengthening of  [1]
[3]:  [[86, 62, 6]] quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[87, 62, 6]] quantum code over GF(2^2)
     ExtendCode [3] 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 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0|0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 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 0 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 0 0|0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 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 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0|0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 0 0 1 0 0 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 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0|0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 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 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0|0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 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 1 1 0 0 0 1 0 0 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 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 1 1 0 1 0|0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 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 1 0 0 1 0 0 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 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0|0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 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 1 1 0 0 0 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 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0|0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 0 1 0]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0 0|0 1 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 1 1 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 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0|0 0 1 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 1 1 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 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0|0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 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 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 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 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0|0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 0 0 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 1 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0|0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 1 1 0 1 0 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 1 0 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0|0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 0|0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 1 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 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0|0 1 1 1 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 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 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 0|0 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 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 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0|0 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 0 0 1 0 0 0 1 1 0 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 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0|0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 0 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 1 0 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0|0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 1 1 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 1 0 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0|0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0]

last modified: 2006-04-03

Notes


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