Bounds on the minimum distance of additive quantum codes

Bounds on [[151,0]]₂

Construction

Construction of a [[151,0,23]] quantum code:
[1]:  [151, 76, 23] Cyclic Linear Code over GF(2)
     cyclic code of length 151 with generating polynomial x^75 + x^74 + x^73 + x^70 + x^67 + x^63 + x^60 + x^59 + x^52 + x^50 + x^48 + x^46 + x^45 + x^40 + x^39 + x^37 + x^36 + x^34 + x^31 + x^30 + x^28 + x^27 + x^25 + x^22 + x^20 + x^19 + x^17 + x^15 + x^14 + x^11 + x^10 + x^8 + x^5 + x^3 + 1
[2]:  [152, 76, 24] Linear Code over GF(2)
     ExtendCode [1] by 1
[3]:  [[152, 0, 24]] CSS self-dual quantum code over GF(2^2)
     CSS code using  [2] and  [2]
[4]:  [[151, 0, 23]] self-dual quantum code over GF(2^2)
     Puncturing of [3] at { 152 }

    stabilizer matrix:

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last modified: 2022-08-08

Notes

• All codes establishing the lower bounds where constructed using MAGMA.
• Most upper bounds on qubit codes for n≤100 are based on a MAGMA program by Eric Rains.
• For n>100, the upper bounds on qubit codes are weak (and not necessarily monotone in k).
• Some additional information can be found in the book by Nebe, Rains, and Sloane.
• My apologies to all authors that have contributed codes to this table for not giving specific credits.