Bounds on the minimum distance of additive quantum codes

Bounds on [[223,175]]₂

Construction

Construction of a [[223,175,8]] quantum code:
[1]:  [[221, 177, 8]] quantum code over GF(2^2)
     QuasiTwistedCyclicCode of length 221 and constant w^2 with generators: x^199 + w*x^198 + w*x^197 + x^195 + w^2*x^194 + w*x^192 + x^191 + x^190 + x^189 + w^2*x^188 + w^2*x^187 + w*x^186 + w^2*x^185 + w*x^182 + w^2*x^181 + x^178 + x^177 + w^2*x^176 + w*x^175 + w*x^174 + x^173 + x^172 + x^170 + w^2*x^169 + x^168 + w*x^167 + w^2*x^166 + w^2*x^165 + x^162 + x^161 + w^2*x^160 + w*x^159 + w^2*x^157 + x^155 + w*x^154 + x^153 + x^152 + x^151 + x^150 + w*x^149 + x^146 + x^145 + w^2*x^144 + w^2*x^143 + w^2*x^142 + w^2*x^141 + w^2*x^136 + w^2*x^135 + w^2*x^134 + x^133 + w*x^132 + w^2*x^131 + w^2*x^130 + w*x^129 + w*x^128 + x^126 + x^124 + w^2*x^122 + x^121 + w^2*x^120 + w*x^119 + x^118 + x^117 + w^2*x^116 + w*x^115 + w^2*x^114 + w*x^113 + w^2*x^112 + w*x^111 + w*x^110 + w^2*x^109 + x^108 + w*x^107 + x^106 + w^2*x^105 + w^2*x^104 + w*x^103 + x^100 + x^97 + w^2*x^96 + w^2*x^95 + x^94 + w^2*x^93 + x^92 + w^2*x^91 + w*x^90 + w^2*x^89 + x^88 + x^87 + x^86 + w*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*x^77 + w^2*x^75 + w*x^73 + x^72 + w^2*x^71 + x^70 + w*x^68 + w^2*x^67 + x^66 + w*x^64 + w^2*x^63 + w*x^62 + w*x^61 + w^2*x^60 + w*x^59 + x^58 + x^57 + w^2*x^56 + w*x^55 + x^54 + x^51 + w*x^50 + x^49 + w^2*x^48 + w^2*x^47 + w^2*x^45 + w^2*x^44 + w^2*x^43 + w*x^41 + w^2*x^40 + w^2*x^39 + w^2*x^38 + w*x^37 + x^36 + x^34 + x^33 + w*x^32 + x^31 + w*x^30 + w^2*x^28 + w*x^27 + x^26 + w*x^25 + w^2*x^24 + w^2*x^23 + w^2*x^21 + x^20 + x^19 + w^2*x^17 + w*x^16 + x^15 + w*x^14 + x^13 + x^12 + w*x^11 + w^2*x^10 + w^2*x^9 + w*x^8 + w^2*x^7 + x^5 + w*x^4 + w^2*x^3 + x^2 + w*x + w
[2]:  [[221, 175, 8]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[223, 175, 8]] quantum code over GF(2^2)
     ExtendCode [2] by 2

    stabilizer matrix:

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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.