Bounds on the minimum distance of additive quantum codes

Bounds on [[243,231]]₂

lower bound:	3
upper bound:	4
Construction

Construction of a [[243,231,3]] quantum code:
[1]:  [[341, 331, 3]] quantum code over GF(2^2)
     cyclic code of length 341 with generating polynomial w*x^340 + w^2*x^339 + x^338 + w*x^337 + w*x^336 + x^335 + x^334 + w^2*x^333 + w^2*x^332 + w^2*x^331 + x^329 + x^328 + x^327 + x^326 + w*x^325 + w*x^324 + w*x^323 + w*x^322 + w*x^321 + x^320 + w*x^318 + x^317 + x^315 + w*x^314 + x^313 + w^2*x^312 + x^311 + w^2*x^310 + w^2*x^309 + w^2*x^307 + w^2*x^305 + w*x^304 + w^2*x^303 + w*x^302 + w^2*x^301 + w*x^300 + x^299 + x^298 + w^2*x^296 + w^2*x^295 + x^293 + w*x^292 + w^2*x^290 + x^289 + w^2*x^288 + w^2*x^287 + x^286 + x^285 + w^2*x^284 + w*x^283 + x^281 + w^2*x^280 + w*x^279 + x^278 + w*x^277 + w*x^276 + w*x^274 + w*x^273 + x^272 + w*x^269 + x^268 + w^2*x^267 + x^266 + w*x^265 + x^264 + w^2*x^263 + w*x^262 + w*x^261 + x^260 + w^2*x^259 + w*x^258 + x^257 + x^255 + x^254 + x^252 + w*x^251 + w*x^250 + w*x^249 + w^2*x^248 + w*x^246 + x^245 + w^2*x^243 + x^242 + x^240 + w*x^239 + x^237 + w*x^236 + w*x^235 + x^234 + w*x^233 + w*x^232 + x^231 + x^229 + w*x^227 + w*x^226 + w^2*x^225 + w*x^222 + x^221 + x^220 + w*x^219 + w^2*x^218 + w^2*x^217 + x^215 + w^2*x^213 + w*x^212 + w^2*x^211 + w^2*x^208 + w^2*x^207 + w*x^206 + w^2*x^205 + x^204 + x^203 + x^202 + w^2*x^200 + x^198 + w^2*x^197 + x^196 + x^195 + w*x^194 + w*x^193 + x^191 + w^2*x^190 + w^2*x^189 + w^2*x^188 + x^187 + w^2*x^186 + w*x^185 + w^2*x^183 + w^2*x^181 + w^2*x^180 + x^179 + x^178 + w*x^177 + w^2*x^175 + x^173 + w^2*x^170 + x^169 + w^2*x^168 + x^167 + w*x^166 + x^164 + x^163 + w^2*x^162 + w^2*x^161 + x^160 + w^2*x^159 + w^2*x^157 + w*x^156 + w*x^155 + w^2*x^152 + w^2*x^151 + w^2*x^150 + x^149 + w*x^148 + w^2*x^146 + w*x^145 + w*x^144 + x^143 + w*x^142 + w*x^140 + x^139 + w^2*x^138 + w^2*x^137 + x^136 + x^134 + x^133 + x^132 + w^2*x^131 + x^130 + w^2*x^129 + x^127 + x^126 + w^2*x^125 + w*x^124 + w^2*x^123 + x^121 + x^120 + w^2*x^118 + x^117 + w^2*x^116 + w^2*x^113 + w^2*x^111 + x^110 + w*x^109 + w^2*x^106 + w*x^104 + w^2*x^103 + x^102 + x^101 + w*x^100 + x^99 + x^98 + w^2*x^97 + w*x^95 + w*x^94 + w*x^93 + w*x^90 + x^89 + w*x^85 + w*x^84 + w^2*x^83 + x^82 + w*x^81 + x^80 + w^2*x^78 + w*x^76 + w*x^75 + w^2*x^74 + w*x^73 + w^2*x^72 + w^2*x^71 + w^2*x^70 + w*x^69 + x^68 + x^67 + x^66 + x^65 + x^63 + w^2*x^62 + x^60 + w*x^59 + w*x^58 + x^55 + w*x^53 + w^2*x^52 + x^51 + w^2*x^50 + x^49 + w^2*x^47 + w^2*x^45 + w^2*x^42 + x^41 + x^40 + w*x^39 + w^2*x^38 + w*x^37 + w*x^36 + w*x^35 + x^34 + x^33 + w*x^31 + x^30 + w^2*x^29 + w*x^26 + w*x^25 + w*x^21 + x^20 + w*x^19 + w^2*x^18 + x^17 + x^15 + w^2*x^13 + x^10 + w*x^9 + x^5 + 1
[2]:  [[243, 233, 3]] quantum code over GF(2^2)
     Shortening of [1] at { 5, 8, 10, 11, 15, 23, 24, 31, 34, 37, 39, 46, 51, 52, 53, 65, 71, 80, 83, 86, 87, 91, 93, 96, 102, 106, 107, 113, 118, 122, 126, 127, 132, 135, 136, 143, 150, 161, 162, 172, 173, 174, 178, 185, 188, 196, 199, 203, 209, 210, 212, 213, 214, 215, 217, 219, 227, 231, 235, 238, 247, 248, 250, 252, 254, 255, 267, 269, 275, 276, 284, 286, 291, 298, 300, 303, 305, 308, 309, 310, 311, 312, 314, 316, 317, 319, 322, 323, 324, 327, 329, 330, 331, 334, 335, 337, 338, 341 }
[3]:  [[243, 231, 3]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 1 1 1|0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1]
      [0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1|1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0]
      [0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0|0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0]
      [0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0|0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0|0 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0]
      [0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0|0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0]
      [0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0|0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0]
      [0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1|0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0]
      [0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0|0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1]

last modified: 2009-02-08
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.
This page is maintained by Markus Grassl (codes@codetables.de). Last change: 10.06.2024
Bounds on the minimum distance of additive quantum codes

Bounds on [[243,231]]2

Construction

Notes

Bounds on [[243,231]]₂
