Bounds on the minimum distance of additive quantum codes

Bounds on [[241,193]]₂

Construction

Construction of a [[241,193,9]] quantum code:
[1]:  [[241, 193, 9]] quantum code over GF(2^2)
     QuasiTwistedCyclicCode of length 241 and constant w with generators: x^217 + w^2*x^216 + w*x^212 + w^2*x^211 + w^2*x^209 + w*x^208 + x^207 + w^2*x^205 + w^2*x^204 + w^2*x^203 + x^202 + w^2*x^201 + w*x^200 + x^199 + x^198 + w*x^197 + x^196 + x^195 + w*x^194 + w^2*x^191 + w^2*x^190 + x^189 + w^2*x^188 + x^187 + w*x^186 + w*x^185 + w*x^183 + x^182 + w*x^180 + w*x^179 + x^178 + x^177 + x^176 + x^175 + w*x^174 + w*x^172 + x^171 + x^170 + w^2*x^169 + x^168 + w^2*x^167 + w^2*x^166 + x^164 + x^160 + x^159 + x^157 + x^156 + w*x^153 + x^150 + w^2*x^149 + x^148 + x^147 + w^2*x^146 + w*x^145 + x^144 + w^2*x^143 + x^142 + w*x^141 + w*x^139 + w^2*x^138 + w^2*x^137 + w*x^136 + x^135 + w^2*x^134 + x^133 + w*x^132 + w*x^131 + w^2*x^130 + w*x^127 + x^126 + w^2*x^124 + x^121 + w*x^120 + x^119 + w*x^118 + x^117 + w*x^115 + w*x^114 + w^2*x^113 + w*x^112 + w^2*x^111 + w*x^109 + w^2*x^108 + w*x^106 + w^2*x^105 + w^2*x^104 + x^103 + w^2*x^102 + w^2*x^100 + w^2*x^99 + x^98 + x^97 + w*x^96 + x^93 + w^2*x^91 + w^2*x^90 + x^87 + w*x^86 + x^85 + w*x^84 + w^2*x^83 + w^2*x^82 + w^2*x^81 + w^2*x^80 + w*x^79 + w^2*x^78 + x^76 + w*x^75 + w^2*x^74 + w^2*x^73 + w^2*x^72 + w^2*x^71 + w^2*x^70 + w*x^69 + w^2*x^68 + w^2*x^67 + x^64 + w^2*x^61 + w*x^60 + w^2*x^58 + w*x^57 + x^53 + x^51 + w^2*x^50 + w^2*x^49 + x^48 + x^47 + w^2*x^46 + w^2*x^45 + x^43 + w*x^42 + x^41 + w^2*x^40 + w*x^39 + w*x^38 + x^37 + x^35 + x^34 + w*x^32 + x^31 + w*x^30 + w^2*x^29 + w^2*x^28 + x^27 + w^2*x^26 + w*x^23 + w^2*x^22 + w*x^21 + w*x^20 + w^2*x^19 + w*x^18 + w*x^17 + w*x^16 + w*x^15 + w^2*x^14 + w*x^13 + x^12 + w^2*x^10 + w^2*x^9 + w^2*x^8 + x^6 + w*x^5 + w*x + w

    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.