Minimum weights of the Gray images for q = 2 and size = 2^5:


To get more detailed infos about the codes, click on the entries in the table.
For an explanation of what the different colors mean, look below.

n68101214161820222426283032343638404244464850525456586062646668707274767880828486889092949698100102104106108110112114116118120122124126128130132134136138140142144146148150152154156158160162164166168170172174176178180182184186188190192194196198200204208212216220224228232236240244248252256260264268272276280284288292296300304308312316320324328332336340344348352356360364368372376380384388392396400408416424432440448456464472480488496
lin. bounds22446889101212141516161718202022232424262728293032323234353637384040414244444647484849505252545556565859606162646464666768697072727374767678798080818284848687888890919293949696969899100101102104106108111112114116119120123125128128131
best22446888101212131416161718202022222424262628293032323234343637384040414244444546484849505252545456565858606162646464666668697072727374767677788080818284848686888890909293949696969898100101100104104108108112114116118120122124128128130132136136138140144144148148152152156156160160164164168168172172176178180182184186188192192194196200200202204208212216220224228232236240244248256
Z16-4+188161624243232404048485656646872768084889296100104108112116120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248256
Z2[X]/(X^2)-2+1+1+1244688891012121416161618202021222424262628293032323234343637384040404242444546484849505252535456565858606162646464666668697072727274747677788080818284848586888890909293949696969898100101
Z2[X]/(X^2)-2+2+122446888101212131416161718202022222424262628283032323234343637384040414244444546484849505252545456565858606062646464666668697072727374767677788080818284848686888890909292949696969898100101
Z2[X]/(X^3)-3+1+14888121616182024242628323236364040444448505254565860646466687272747680808284888890929696100100104104108108112114116118120122124128128130132136136138140144144146148152152154156160160164164168168172172176178180182184186188192192194196200200202
Z2[X]/(X^3)-3+2248810121616202024242828323236364040444448505254565860646466687272747680808484888892929696100100104104108108112114116118120122124128128130132136136138140144144148148152152156156160160164164168168172172176178180182184186188192192194196200200202
Z2[X]/(X^4)-4+188161624243232404048485656646872768084889296100104108112116120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248256
Z4-2+1+1+1244688891012121416161618202021222424262628293032323234343637384040404242444546484849505252535456565858606162646464666668697072727274747677788080818284848586888890909293949696969898100101
Z4-2+2+122446888101212131416161718202022222424262628283032323234343637384040414244444546484849505252545456565858606062646464666668697072727374767677788080818284848686888890909292949696969898100101
Z4[X]/(X^2+2)-4+188161624243232404048485656646872768084889296100104108112116120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248256
Z4[X]/(X^2+2,X^3)-3+1+14888121616182024242628323236364040444448505254565860646466687272747680808284888890929696100100104104108108112114116118120122124128128130132136136138140144144146148152152154156160160164164168168172172176178180182184186188192192194196200200202
Z4[X]/(X^2+2,X^3)-3+2248810121616202024242828323236364040444448505254565860646466687272747680808484888892929696100100104104108108112114116118120122124128128130132136136138140144144148148152152156156160160164164168168172172176178180182184186188192192194196200200202
Z4[X]/(X^2+2X+2)-4+188161624243232404048485656646872768084889296100104108112116120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248256
Z4[X]/(X^3+2,X^4)-4+188161624243232404048485656646872768084889296100104108112116120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248256
Z8-3+1+14888121616182024242628323236364040444448505254565860646466687272747680808284888890929696100100104104108108112114116118120122124128128130132136136138140144144146148152152154156160160164164168168172172176178180182184186188192192194196200200202
Z8-3+2248810121616202024242828323236364040444448505254565860646466687272747680808484888892929696100100104104108108112114116118120122124128128130132136136138140144144148148152152156156160160164164168168172172176178180182184186188192192194196200200202

The color scheme indicates how the minimum distance of the Gray image compares to that of the best known linear codes over GF(2). It is as follows:
d There are linear codes over GF(2) with minimum distance higher than d.
d The best known linear codes over GF(2) have minimum distance d.
d It is possible that there are linear codes over GF(2) with minimum distance d or higher, but none is known yet (BTKL=better-than-known-linear).
d There are no linear codes over GF(2) with minimum distance d or higher (BTL=better-than-linear).
d There was no information about the corresponding linear codes over GF(2) in the database.

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