Bounds on the minimum distance of additive quantum codes
Bounds on [[243,217]]2
| lower bound: | 5 |
| upper bound: | 7 |
Construction
Construction of a [[243,217,5]] quantum code:
[1]: [[241, 217, 5]] quantum code over GF(2^2)
cyclic code of length 241 with generating polynomial x^229 + w*x^228 + w*x^227 + w*x^226 + x^225 + w*x^222 + w*x^221 + w^2*x^220 + w*x^219 + w^2*x^218 + w*x^217 + w*x^216 + w^2*x^215 + x^214 + x^213 + x^212 + x^210 + x^209 + w*x^207 + w^2*x^205 + w*x^203 + x^201 + w^2*x^200 + x^199 + w^2*x^198 + w*x^197 + w^2*x^196 + w*x^195 + x^193 + w^2*x^192 + w^2*x^191 + w*x^190 + x^189 + w^2*x^188 + x^187 + x^186 + x^185 + w^2*x^184 + w*x^182 + x^181 + x^178 + w^2*x^177 + w*x^176 + x^175 + w*x^174 + w^2*x^173 + x^172 + w^2*x^171 + x^170 + w^2*x^169 + w*x^168 + x^167 + w^2*x^166 + w^2*x^165 + x^164 + w^2*x^163 + x^161 + w^2*x^160 + w*x^159 + w*x^158 + w^2*x^157 + w*x^155 + w*x^154 + w^2*x^153 + x^151 + w^2*x^150 + w^2*x^149 + w^2*x^148 + w*x^147 + x^145 + w*x^143 + w*x^142 + x^140 + x^139 + w^2*x^138 + w*x^137 + x^136 + w*x^134 + w*x^133 + w*x^130 + w*x^128 + w^2*x^127 + w^2*x^126 + x^125 + w*x^124 + w*x^123 + x^122 + w*x^121 + w*x^120 + x^119 + w*x^118 + x^117 + w^2*x^116 + w^2*x^115 + w^2*x^114 + w^2*x^113 + x^112 + w*x^111 + x^110 + w*x^109 + w*x^108 + x^107 + w*x^106 + w*x^105 + x^104 + w^2*x^103 + w^2*x^102 + w*x^101 + w*x^99 + w*x^96 + w*x^95 + x^93 + w*x^92 + w^2*x^91 + x^90 + x^89 + w*x^87 + w*x^86 + x^84 + w*x^82 + w^2*x^81 + w^2*x^80 + w^2*x^79 + x^78 + w^2*x^76 + w*x^75 + w*x^74 + w^2*x^72 + w*x^71 + w*x^70 + w^2*x^69 + x^68 + w^2*x^66 + x^65 + w^2*x^64 + w^2*x^63 + x^62 + w*x^61 + w^2*x^60 + x^59 + w^2*x^58 + x^57 + w^2*x^56 + w*x^55 + x^54 + w*x^53 + w^2*x^52 + x^51 + x^48 + w*x^47 + w^2*x^45 + x^44 + x^43 + x^42 + w^2*x^41 + x^40 + w*x^39 + w^2*x^38 + w^2*x^37 + x^36 + w*x^34 + w^2*x^33 + w*x^32 + w^2*x^31 + x^30 + w^2*x^29 + x^28 + w*x^26 + w^2*x^24 + w*x^22 + x^20 + x^19 + x^17 + x^16 + x^15 + w^2*x^14 + w*x^13 + w*x^12 + w^2*x^11 + w*x^10 + w^2*x^9 + w*x^8 + w*x^7 + x^4 + w*x^3 + w*x^2 + w*x + 1
[2]: [[243, 217, 5]] quantum code over GF(2^2)
ExtendCode [1] by 2
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0]
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last modified: 2024-05-23
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