Bounds on the minimum distance of additive quantum codes

Bounds on [[166,0]]₂

Construction

Construction of a [[166,0,22]] quantum code:
[1]:  [167, 84, 23] Cyclic Linear Code over GF(2)
     cyclic code of length 167 with generating polynomial x^83 + x^82 + x^79 + x^77 + x^75 + x^73 + x^71 + x^70 + x^66 + x^64 + x^60 + x^59 + x^58 + x^57 + x^56 + x^54 + x^52 + x^51 + x^50 + x^48 + x^47 + x^43 + x^41 + x^38 + x^37 + x^36 + x^34 + x^33 + x^31 + x^30 + x^27 + x^24 + x^23 + x^21 + x^19 + x^16 + x^13 + x^12 + x^10 + x^7 + x^5 + x^2 + 1
[2]:  [168, 84, 24] Linear Code over GF(2)
     ExtendCode [1] by 1
[3]:  [[168, 0, 24]] CSS self-dual quantum code over GF(2^2)
     CSS code using  [2] and  [2]
[4]:  [[166, 0, 22]] self-dual quantum code over GF(2^2)
     Puncturing of [3] at { 167 .. 168 }

    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.