Bounds on the minimum distance of additive quantum codes

Bounds on [[228,163]]₂

Construction

Construction of a [[228,163,9]] quantum code:
[1]:  [[219, 165, 9]] quantum code over GF(2^2)
     QuasiTwistedCyclicCode of length 219 and constant w^2 with generators: x^192 + x^190 + w*x^188 + x^187 + x^186 + w^2*x^185 + x^183 + w^2*x^182 + x^181 + w^2*x^178 + w*x^176 + w*x^175 + w^2*x^174 + x^172 + x^171 + w*x^170 + w*x^168 + w*x^167 + w^2*x^165 + x^164 + w^2*x^161 + x^159 + w^2*x^158 + w*x^156 + w^2*x^155 + w^2*x^154 + w*x^152 + x^151 + x^149 + w^2*x^148 + x^147 + x^146 + w^2*x^145 + x^144 + w^2*x^142 + w^2*x^140 + w^2*x^139 + w^2*x^138 + x^137 + x^136 + w*x^134 + w^2*x^132 + x^131 + w*x^130 + w*x^129 + w*x^128 + x^127 + x^126 + w^2*x^125 + x^124 + w*x^123 + w*x^122 + x^121 + w^2*x^120 + x^118 + x^117 + w^2*x^114 + w*x^113 + w*x^110 + x^109 + w^2*x^108 + x^107 + w*x^106 + w*x^105 + w^2*x^104 + w^2*x^103 + w*x^100 + w*x^96 + w^2*x^95 + w^2*x^94 + x^92 + w*x^91 + x^90 + w^2*x^89 + w^2*x^88 + w^2*x^87 + x^86 + x^85 + w^2*x^83 + w*x^82 + w*x^81 + x^80 + w*x^79 + w*x^78 + w*x^77 + w^2*x^76 + w^2*x^75 + w^2*x^73 + w*x^72 + w^2*x^71 + x^70 + w^2*x^68 + w^2*x^67 + w*x^66 + x^65 + w*x^64 + w^2*x^63 + x^62 + w^2*x^61 + w*x^60 + w*x^59 + x^58 + w^2*x^57 + x^55 + w^2*x^54 + w*x^52 + w^2*x^51 + x^48 + w*x^46 + w^2*x^45 + w*x^44 + w^2*x^43 + w*x^42 + w^2*x^39 + x^37 + x^36 + w^2*x^34 + w*x^32 + x^31 + w^2*x^30 + w^2*x^29 + w^2*x^28 + w*x^27 + w*x^25 + x^23 + w^2*x^22 + w*x^20 + w*x^19 + w^2*x^17 + w^2*x^16 + w^2*x^15 + w*x^14 + w^2*x^13 + x^12 + w^2*x^10 + w^2*x^9 + x^8 + w*x^7 + x^6 + x^5 + w*x^2 + w^2
[2]:  [[219, 163, 9]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[228, 163, 9]] quantum code over GF(2^2)
     ExtendCode [2] by 9

    stabilizer matrix:

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last modified: 2024-10-16

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.