Minimum weights of the Gray images for q = 2 and size = 2^7:


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.

n8101214161820222426283032343638404244464850525456586062646668707274767880828486889092949698100102104106108110112114116118120122124126128130132134136138140142144146148150152154156158160162164166168170172174176178180182184186188190192194196198200204208212216220224228232236240244248252256260264268272276280284288292296300304308312316320324328332336340344348352356360364368372376380384388392396400408416424432440448456464472480488496
lin. bounds224467881011121214151616181920212224242426272830323232333435363738404041424445464848485051525354565657586060626364646465666868707172727475767778808080828384858688888990929294959696969899101104105108110112113116118120122124126128
best224466881010121214141616181820202224242426282830323232323434363638404041424444464848484950525254565656575860616264646465666868707072727374767678808080828284848688888890929293949696969898100104104106108112112114116120120122124128128130132136136138140144144146148152152154156160160162164168168170172176176180180184184188188192192196196200200208208216216224224232232240240248
Z16-4+1+1+1816162432323236404848566464647272808488969696104104112116120128128132136140144148152160160164168172176180184192192196200204208212216224224228232236240244
Z16-4+2+188161624323232404048485664646472728084889696100104108112116120128128132136144144148152160160164168176176180184192192196200208208212216224224228232240240244
Z16-4+34812162024323236404448525664646872808084889696100104112112116120128128132136144144148152160160164168176176180184192192200200208208216216224224232232240240248
Z2[X]/(X^2)-2+1+1+1+1+1244468881012121416161616182020212224242628303232323232333436363840404042424445464848484950525254565656586062646464646465666868707272727474767778808080818284848688888890929496969696
Z2[X]/(X^2)-2+2+1+1+124446888101212121416161618202020222424242628283032323233343636373840404244444648484848505052535456565758606162646464646666686869707272737476787880808082828485858788899092939496969696
Z2[X]/(X^2)-2+2+2+12244668810101212141416161818202022242424262628293032323234343636384040414244444546484849505252545656565758606162646464656668686970727273747676788080808282848486888888909292939496969698
Z2[X]/(X^3)-3+1+1+1+1488812161616202428323232323436404042444850525656606464646468727274768080828488909296969698100104104106108112112114116120122124128128128132134136136138140144144146148152154156160160160164166168168170172176176178180184186188192192192196
Z2[X]/(X^3)-3+2+1+1448812161616202024283232323436384042444848505256586064646466687272768080808284889092969696100100104106108112112114116116120122124128128130132134136138140144144146148150152154156160160162164168168170172176176178180184184186188192192194196
Z2[X]/(X^3)-3+2+224681012161618202224283232323436404042444848505256566064646468687272768080808484889092969696100104104106108112112114116120120122124128128128132136136138140144144146148152152154156160160160164168168170172176176178180184184186188192192192196
Z2[X]/(X^3)-3+3+144881012161620202424283232323636404044484848525256586064646468687272768080808484889092969698100104104106108112112114116120120122124128128130132136136138140144144146148152152154156160160162164168168170172176176180180184184188188192192196196
Z2[X]/(X^4)-4+1+1+1816162432323236404848566464647272808488969696104104112116120128128132136140144148152160160164168172176180184192192196200204208212216224224228232236240244
Z2[X]/(X^4)-4+2+188161624323232404048485664646472728084889696100104108112116120128128132136144144148152160160164168176176180184192192196200208208212216224224228232240240244
Z2[X]/(X^4)-4+34812162024323236404448525664646872808084889696100104112112116120128128132136144144148152160160164168176176180184192192200200208208216216224224232232240240248
Z4-2+1+1+1+1+1244468881012121416161616182020212224242628303232323232323436363840404041424445464848484950525254565656586062646464646464666868707272727374767778808080818284848688888890929496969696
Z4-2+2+1+1+124446888101212121416161618202020222424242628283032323233343636373840404244444648484848495052535456565758606162646464646666686869707272737476787880808082828485858788899092929496969696
Z4-2+2+2+12244668810101212141416161818202022242424262828293032323234343636384040414244444546484849505252545656565758606162646464656668687070727273747676788080808282848486888888909292939496969698
Z4[X]/(X^2+2)-4+1+1+1816162432323236404848566464647272808488969696104104112116120128128132136140144148152160160164168172176180184192192196200204208212216224224228232236240244
Z4[X]/(X^2+2)-4+2+188161624323232404048485664646472728084889696100104108112116120128128132136144144148152160160164168176176180184192192196200208208212216224224228232240240244
Z4[X]/(X^2+2)-4+34812162024323236404448525664646872808084889696100104112112116120128128132136144144148152160160164168176176180184192192200200208208216216224224232232240240248
Z4[X]/(X^2+2,X^3)-3+1+1+1+1488812161616202428323232323436404042444850525656606464646468727274768080828488909296969698100104104106108112112114116120122124128128128132134136136138140144144146148152154156160160160164166168168170172176176178180184186188192192192196
Z4[X]/(X^2+2,X^3)-3+2+1+1448812161616202024283232323436384042444848505256586064646466687272768080808284889092969696100100104106108112112114116116120122124128128130132134136138140144144146148150152154156160160162164168168170172176176178180184184186188192192194196
Z4[X]/(X^2+2,X^3)-3+2+224681012161618202224283232323436404042444848505256566064646468687272768080808484889092969696100104104106108112112114116120120122124128128128132136136138140144144146148152152154156160160160164168168170172176176178180184184186188192192192196
Z4[X]/(X^2+2,X^3)-3+3+144881012161620202424283232323636404044484848525256586064646468687272768080808484889092969698100104104106108112112114116120120122124128128130132136136138140144144146148152152154156160160162164168168170172176176180180184184188188192192196196
Z4[X]/(X^2+2X+2)-4+1+1+1816162432323236404848566464647272808488969696104104112116120128128132136140144148152160160164168172176180184192192196200204208212216224224228232236240244
Z4[X]/(X^2+2X+2)-4+2+188161624323232404048485664646472728084889696100104108112116120128128132136144144148152160160164168176176180184192192196200208208212216224224228232240240244
Z4[X]/(X^2+2X+2)-4+34812162024323236404448525664646872808084889696100104112112116120128128132136144144148152160160164168176176180184192192200200208208216216224224232232240240248
Z4[X]/(X^3+2,X^4)-4+1+1+1816162432323236404848566464647272808488969696104104112116120128128132136140144148152160160164168172176180184192192196200204208212216224224228232236240244
Z4[X]/(X^3+2,X^4)-4+2+188161624323232404048485664646472728084889696100104108112116120128128132136144144148152160160164168176176180184192192196200208208212216224224228232240240244
Z4[X]/(X^3+2,X^4)-4+34812162024323236404448525664646872808084889696100104112112116120128128132136144144148152160160164168176176180184192192200200208208216216224224232232240240248
Z8-3+1+1+1+1488812161616202428323232323436404042444850525656606464646468727274768080828488909296969698100104104106108112112114116120122124128128128132134136136138140144144148148152154156160160160164166168168170172176176180180184186188192192192196
Z8-3+2+1+1448812161616202024283232323436384042444848505256586064646466687272768080808284889092969696100100104106108112112114116116120122124128128130132134136138140144144146148150152154156160160162164168168170172176176178180184184186188192192194196
Z8-3+2+224681012161618202224283232323436384044444848505256566064646468687272768080808484889092969696100104104104108112112114116120120122124128128128132136136138140144144146148152152154156160160160164168168170172176176178180184184186188192192194196
Z8-3+3+144881012161620202424283232323636404044484848525256586064646468687272768080808484889092969698100104104106108112112114116120120122124128128130132136136138140144144146148152152154156160160162164168168170172176176180180184184188188192192196196

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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