Minimum weights of the Gray images for q = 2 and size = 2^18:


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.

n4048566472808896104112120128136144152160168176184192200208216224232240248256264272280288296304312320328336344352360368376384392400408416424432440448456464472480488496
lin. bounds10-1112-1416-192224-2628-3030-3534-3938-4241-4644-5048-5452-5856-6261-6664-7067-7472-7874-8280-8681-8986-9388-9892-10296-105102-109108-114112-118
best488161620242832364044484852566064687276808488889296100104108112116120124128132136140144144148152156160164168172176180184188192196200204208212216
Z16-4+4+4+4+2488161620242832364044484852566064687276808484889296100104108112116120124128132136136144144148152156160164168172176180184188192196196200208212212
Z2[X]/(X^4)-4+4+4+4+288161620242832364044484852566064687276808488889296100104108112116120124128132136140144144148152156160164168172176180184188192196200204208212216
Z4[X]/(X^2+2)-4+4+4+4+2488161620242832364044484852566064687276808488889296100104108112116120124128132136140144144148152156160164168172176180184188192196196204208212212
Z4[X]/(X^2+2X+2)-4+4+4+4+2488161620242832364044484852566064687276808488889296100104108112116120124128132132136144144148152156160164168172176180184188192196196204204212212
Z4[X]/(X^3+2,X^4)-4+4+4+4+2488161620242832364044484852566064687276808488889296100104108112116120124128132136140144144148152156160164168172176180184188192196200204204212212

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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