Minimum weights of the Gray images for q = 3 and size = 3^12:


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.

n3645546372819099108117126135144153162171180189198207216225234243252261270279288297306315324333342351360369378387396405414423432441450459468477486495
lin. bounds15-1720-2325-2830-3536-4042-4647-5252-5857-6463-7069-7575-8180-8785-9391-9996-105103-111108-117114-123120-129126-136132-142138-147144-153
best612182430363945515760667278849096102108114120126129135141147153159165171177183189195198204210216222228234240246252258264270276279285291297
Z27-3+3+3+3612182430363945515760667278849096102108114120126129135141147153159165171177183189195198204210216222228234240246252258264270276279285291297
Z3[X]/(X^3)-3+3+3+3612182430363945515760667278849096102108114120126129135141147153159165171177183189195198204210216222228234240246252258264270273279285291297
Z9[X]/(X^2+3,X^3)-3+3+3+3612182430363945515760667278849096102108114120123129135141147153159165171177183189195198204210216222228234240246252258264270276279285291297
Z9[X]/(X^2+6,X^3)-3+3+3+3612182430363945515760667278849096102108114120126129135141147153159165171177183189195198204210216222228234240246252258264270273279285291297

The color scheme indicates how the minimum distance of the Gray image compares to that of the best known linear codes over GF(3). It is as follows:
d There are linear codes over GF(3) with minimum distance higher than d.
d The best known linear codes over GF(3) have minimum distance d.
d It is possible that there are linear codes over GF(3) with minimum distance d or higher, but none is known yet (BTKL=better-than-known-linear).
d There are no linear codes over GF(3) with minimum distance d or higher (BTL=better-than-linear).
d There was no information about the corresponding linear codes over GF(3) in the database.

Back to main page