Minimum weights of the Gray images for q = 3 and size = 3^6:


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.

n9121518212427303336394245485154576063666972757881848790939699102105108111114117120123126129132135138141144147150153156159162165168171174177180183186189192195198201204207210213216219222225228231234237240243246249252255258261264267270273276279282285288291294297306315324333342351360369378387396405414423432441450459468477486495
lin. bounds36791113151718-19212325272931343636-373941-4242-434547-4849-50515454-555759-60616365-66676972737578808183-8485-8687-889090-929395-9697-9899-100102104106108109111114115-116117119-120121-122124126127-128129-130132134135137-138139-140141-142144145-146147-148150152154-155156159162
best2468101215151820222427283032343638404245474851545456586063646669707275767881838487909093949699101102105108108110112114117119120123126126129131132135137138141144144147149150153156159162162163165168168171174175177180181183186187189192193195201207216216222228234240246252261267273279285288297303309315324327
Z27-3+1+1+191818273645545454637281819099108108108117126135144153162162162168177180189189198207216216225231234243243252261270270279279288297306315324324
Z27-3+2+19121827333645545463727281879099108111117126129135144153162162165171180183189195201207216219225234237243252255261270273279288291297306309315324
Z27-3+36121824303642485460667278849096105108114120126132141144153162165171177183189195201207216216222228234240246252261267273279285288297303309315324327
Z3[X]/(X^2)-2+1+1+1+136691215181818212427273033363636394245454851545454576063636669727272757881818487909090939699100103105108108108111114117117120123126126126129132135135138141141144147150153156159162162162162162165168168171174177180180180183186189189192
Z3[X]/(X^2)-2+2+1+13669121215181821242427303133363639424345484951545557606264666969727375787981848587909193969799102103105108109111114115117120121123126127129132135135138139144144147148150151154156158161162163166168171173175177179180182184186189191193195
Z3[X]/(X^2)-2+2+22468101215151820222427283032333638404245464851545456586063646668707274767881828487909093949699101102105108108110112114117119120123126126129131132135137138141143144146149150153155156159161163165168168171174174177180181183186187189192193195
Z3[X]/(X^3)-3+1+1+191818273645545454637281819099108108108117126135144153162162162168177180189189198207216216225231234243243252261270270279279288297306315324324
Z3[X]/(X^3)-3+2+19121827333645545463727281879099108111117126129135144153162162165171180183189195201207216219225234237243252255261270273279288291297306309315324
Z3[X]/(X^3)-3+36121824303642485460667278849096105108114120126132141144153162165171177183189195201207216216222228234240246252261267273279285288297303309315324327
Z9-2+1+1+1+136691215181818212427273033363636394245454851545454576063636669727272757881818487909090939699100103105108108108111114117117120123126126126129132135135138141141144147150153156159162162162162162165168168171174177180180180183186189189192
Z9-2+2+1+13669121215181821242427303133363639424345484951545557606264666969727375787981848587909193969799102103105108109111114115117120121123126127129132135135138139144144147148150151154156158161162163166168171173175177179180182184186189191193195
Z9-2+2+22468101215151820222427283032343638404245474851545456586063646668707275767881838487899093949699101102105108108110112114117119120123125126129130132135137138141143144146149150153155156159161163165167168171173174177180181183186187189192193195
Z9[X]/(X^2+3,X^3)-3+1+1+191818273645545454637281819099108108108117126135144153162162162168177180189189198207216216225231234243243252261270270279279288297306315324324
Z9[X]/(X^2+3,X^3)-3+2+19121827333645545463727281879099108111117126129135144153162162165171180183189195201207216219225234237243252255261270273279288291297306309315324
Z9[X]/(X^2+3,X^3)-3+36121824303642485460667278849096105108114120126132141144153162165171177183189195201207216216222228234240246252261267273279285288297303309315324327
Z9[X]/(X^2+6,X^3)-3+1+1+191818273645545454637281819099108108108117126135144153162162162168177180189189198207216216225231234243243252261270270279279288297306315324324
Z9[X]/(X^2+6,X^3)-3+2+19121827333645545463727281879099108111117126129135144153162162165171180183189195201207216219225234237243252255261270273279288291297306309315324
Z9[X]/(X^2+6,X^3)-3+36121824303642485460667278849096105108114120126132141144153162165171177183189195201207216216222228234240246252261267273279285288297303309315324327

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.

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