Minimum weights of the Gray images for q = 2 and size = 2^4:


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.

n468101214161820222426283032343638404244464850525456586062646668707274767880828486889092949698100102104106108110112114116118120122124126128130132134136138140142144146148150152154156158160162164166168170172174176178180182184186188190192194196198200204208212216220224228232236240244248252256260264268272276280284288292296300304308312316320324328332336340344348352356360364368372376380384388392396
lin. bounds12446788101112131416161718202022232424262728293032323334363638394040424344454648484950525254555656585960616264646566686870717272747576777880808182848486878888909192939496969798100100102103104104106108110112114116119120123125128129132134136
best12446688101012131416161718202022222424262628293032323334363638384040424244454648484950525254545656585860616264646566686870707272747476777880808182848486868888909092939496969798100100102102104104104108108112114116118120122124128128132132136136140140144146148150152154156160160164164168168172172176178180182184186188192192196196200200204204208210
Z2[X]/(X^2)-2+1+12444688101012131416161718202021222424262628293032323334363637384040424244454648484950525253545656585860616264646566686869707272747476777880808182848485868888909092939496969798100100101102104104
Z2[X]/(X^2)-2+22446688101012121416161718202022222424262628293032323334363638384040424244454648484950525254545656585860616264646566686870707272747476777880808182848486868888909092939496969798100100102102104104
Z2[X]/(X^3)-3+144881212161820222426283232363640404444485052545658606464686872727676808284868890929696100100104104108108112114116118120122124128128132132136136140140144146148150152154156160160164164168168172172176178180182184186188192192196196200200204204208210
Z4-2+1+12444688101012131416161718202021222424262628293032323334363637384040424244454648484950525253545656585860616264646566686869707272747476777880808182848485868888909092939496969798100100101102104104
Z4-2+212446688101012121416161718202022222424262628293032323334363638384040424244454648484950525254545656585860616264646566686870707272747476777880808182848486868888909092939496969798100100102102104104
Z4[X]/(X^2+2,X^3)-3+144881212161820222426283232363640404444485052545658606464686872727676808284868890929696100100104104108108112114116118120122124128128132132136136140140144146148150152154156160160164164168168172172176178180182184186188192192196196200200204204208210
Z8-3+144881212161820222426283232363640404444485052545658606464686872727676808284868890929696100100104104108108112114116118120122124128128132132136136140140144146148150152154156160160164164168168172172176178180182184186188192192196196200200204204208210

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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