Bounds on the minimum distance of additive quantum codes

Bounds on [[119,108]]2

lower bound:3
upper bound:4

Construction

Construction of a [[119,108,3]] 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]:  [[118, 108, 3]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 22, 24, 28, 30, 31, 32, 35, 37, 38, 41, 43, 44, 45, 49, 50, 51, 52, 53, 54, 55, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 73, 78, 79, 80, 84, 85, 87, 90, 92, 93, 94, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 111, 112, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 137, 140, 141, 142, 143, 144, 145, 146, 150, 151, 153, 156, 157, 159, 160, 162, 163, 165, 166, 167, 169, 172, 173, 175, 176, 177, 178, 179, 180, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 203, 204, 207, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 232, 233, 234, 235, 236, 239, 240, 241, 242, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 258, 260, 262, 263, 264, 265, 268, 271, 272, 276, 278, 279, 280, 281, 283, 284, 286, 287, 288, 297, 298, 299, 300, 302, 303, 304, 305, 306, 308, 309, 310, 311, 313, 315, 318, 319, 322, 323, 324, 325, 326, 328, 329, 330, 331, 333, 335, 336, 337, 338, 339, 340 }
[3]:  [[119, 108, 3]] quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014