Bounds on the minimum distance of additive quantum codes

Bounds on [[241,193]]₂

Construction

Construction of a [[241,193,8]] quantum code:
[1]:  [[241, 193, 8]] quantum code over GF(2^2)
     cyclic code of length 241 with generating polynomial x^217 + w*x^216 + w*x^215 + w*x^214 + x^213 + w^2*x^209 + w^2*x^208 + w^2*x^207 + w^2*x^205 + w^2*x^203 + w*x^202 + w^2*x^201 + x^200 + w^2*x^199 + w*x^198 + x^197 + w^2*x^196 + w*x^195 + x^194 + w*x^193 + w^2*x^192 + w*x^191 + x^190 + w^2*x^189 + w^2*x^188 + x^187 + w^2*x^186 + w^2*x^184 + w*x^182 + w^2*x^181 + w*x^180 + x^178 + x^175 + w^2*x^172 + w*x^171 + x^170 + x^167 + x^166 + x^163 + w^2*x^162 + x^161 + w^2*x^160 + w*x^159 + x^158 + w^2*x^156 + x^155 + w^2*x^154 + w*x^153 + x^150 + w*x^149 + x^148 + w*x^147 + x^146 + w^2*x^145 + w*x^144 + w^2*x^143 + w^2*x^142 + w*x^141 + x^140 + w*x^139 + x^138 + w^2*x^136 + w^2*x^133 + w^2*x^132 + x^131 + w*x^130 + w*x^128 + w^2*x^127 + x^126 + x^125 + w*x^124 + x^123 + w*x^122 + w^2*x^121 + w*x^120 + w*x^119 + w*x^118 + w*x^117 + w^2*x^115 + w^2*x^114 + w*x^113 + x^112 + w^2*x^111 + x^109 + x^108 + w^2*x^106 + x^105 + w*x^104 + w^2*x^103 + w^2*x^102 + w*x^100 + w*x^99 + w*x^98 + w*x^97 + w^2*x^96 + w*x^95 + x^94 + w*x^93 + x^92 + x^91 + w^2*x^90 + w*x^89 + w*x^87 + x^86 + w^2*x^85 + w^2*x^84 + w^2*x^81 + x^79 + w*x^78 + x^77 + w*x^76 + w^2*x^75 + w^2*x^74 + w*x^73 + w^2*x^72 + x^71 + w*x^70 + x^69 + w*x^68 + x^67 + w*x^64 + w^2*x^63 + x^62 + w^2*x^61 + x^59 + w*x^58 + w^2*x^57 + x^56 + w^2*x^55 + x^54 + x^51 + x^50 + x^47 + w*x^46 + w^2*x^45 + x^42 + x^39 + w*x^37 + w^2*x^36 + w*x^35 + w^2*x^33 + w^2*x^31 + x^30 + w^2*x^29 + w^2*x^28 + x^27 + w*x^26 + w^2*x^25 + w*x^24 + x^23 + w*x^22 + w^2*x^21 + x^20 + w*x^19 + w^2*x^18 + x^17 + w^2*x^16 + w*x^15 + w^2*x^14 + w^2*x^12 + w^2*x^10 + w^2*x^9 + w^2*x^8 + x^4 + w*x^3 + w*x^2 + w*x + 1

    stabilizer matrix:

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last modified: 2024-04-24

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.