Minimum weights of the Gray images for q = 2 and size = 2^6:


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. bounds12345688910121214161616181820212224242526282830313232323435363738404041424444464748484950525254555656585960616264646465666868707172727475767778808080828384858688888990929294959696969899100102104106108111112114116119120123125128128
best12346688910121214161616181820202224242426282829303232323434363638404040424444454648484950525254545656585860616264646465666868707072727474767778808080828284858688888990929293949696969898100100104104108108112114116118120122124128128130132134136138140144144146148152152154156160160162164168168170172176176180180184184188188192192196196200200204208212216220224228232236240244248
Z16-4+1+1816162024323236404848525664646872808084889696100104112112116120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248
Z16-4+24816162024323236404848525664647272808088889696104104112112120120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248
Z2[X]/(X^2)-2+1+1+1+124446888101214161616161718202021222425262829303232323234363638404040414244454648484850525253545656585860616264646464666868697072727374767778808080818284848586888890909293949696969898
Z2[X]/(X^2)-2+2+1+12244688810121214161616171820202224242425262829303232323434363638404040424444454648484950525254545656585860616264646465666868707072727474767778808080828284858688888890909293949696969898
Z2[X]/(X^2)-2+2+212345688910121214161616181820202224242426282829303232323434363638404040424444454648484950525254545656585860616264646465666868707072727474767778808080828284858688888990929293949696969898
Z2[X]/(X^3)-3+1+1+148812161616182024242832323236364042444848485252565860646466687272747680808284888890929696100100104104108108112114116118120122124128128130132134136138140144144146148150152154156160160162164166168170172176176178180182184186188192192194196200
Z2[X]/(X^3)-3+2+1448812161616202024262832323236404042444848505256565860646466687272747680808484888892929696100100104104108108112114116118120122124128128130132134136138140144144146148150152154156160160162164168168170172176176178180184184186188192192194196200
Z2[X]/(X^3)-3+324681012161618202424262832323436404042444848525256566060646468687272767680808484888892929696100100104104108108112114116118120122124128128130132134136138140144144146148152152154156160160162164168168170172176176180180184184188188192192196196200
Z2[X]/(X^4)-4+1+1816162024323236404848525664646872808084889696100104112112116120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248
Z2[X]/(X^4)-4+24816162024323236404848525664647272808088889696104104112112120120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248
Z4-2+1+1+1+124446888101214161616161718202021222425262828303232323234363638404040414244454648484850525253545656585860616264646464666868697072727374767778808080818284848586888890909293949696969898
Z4-2+2+1+12244688810121214161616171820202224242425262829303232323434363638404040424444454648484950525254545656585860616264646465666868707072727474767778808080828284858688888890909293949696969898
Z4-2+2+212346688910121214161616181820202224242426282829303232323434363638404040424444454648484950525254545656585860616264646465666868707072727474767778808080828284858688888990929293949696969898
Z4[X]/(X^2+2)-4+1+1816162024323236404848525664646872808084889696100104112112116120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248
Z4[X]/(X^2+2)-4+24816162024323236404848525664647272808088889696104104112112120120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248
Z4[X]/(X^2+2,X^3)-3+1+1+148812161616182024242832323236364042444848485252565860646466687272747680808284888890929696100100104104108108112114116118120122124128128130132134136138140144144146148150152154156160160162164166168170172176176178180182184186188192192194196200
Z4[X]/(X^2+2,X^3)-3+2+1448812161616202024262832323236404042444848505256565860646466687272747680808484888892929696100100104104108108112114116118120122124128128130132134136138140144144146148150152154156160160162164168168170172176176178180184184186188192192194196200
Z4[X]/(X^2+2,X^3)-3+324681012161618202424262832323436404042444848525256566060646468687272767680808484888892929696100100104104108108112114116118120122124128128130132134136138140144144146148152152154156160160162164168168170172176176180180184184188188192192196196200
Z4[X]/(X^2+2X+2)-4+1+1816162024323236404848525664646872808084889696100104112112116120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248
Z4[X]/(X^2+2X+2)-4+24816162024323236404848525664647272808088889696104104112112120120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248
Z4[X]/(X^3+2,X^4)-4+1+1816162024323236404848525664646872808084889696100104112112116120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248
Z4[X]/(X^3+2,X^4)-4+24816162024323236404848525664647272808088889696104104112112120120128128136136144144152152160160168168176176184184192196200204208212216220224228232236240244248
Z8-3+1+1+148812161616182024242832323236364042444848485252565860646466687272747680808284888890929696100100104104108108112114116118120122124128128130132134136138140144144146148150152154156160160162164166168170172176176178180182184186188192192194196200
Z8-3+2+1448812161616202024262832323236404042444848505256565860646466687272747680808484888892929696100100104104108108112114116118120122124128128130132134136138140144144146148150152154156160160162164168168170172176176178180184184186188192192194196200
Z8-3+324681012161618202424262832323436404042444848525256566060646468687272767680808484888892929696100100104104108108112114116118120122124128128130132134136138140144144146148152152154156160160162164168168170172176176180180184184188188192192196196200

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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