Minimum weights of the Gray images for q = 3 and size = 3^8:


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.

n121518212427303336394245485154576063666972757881848790939699102105108111114117120123126129132135138141144147150153156159162165168171174177180183186189192195198201204207210213216219222225228231234237240243246249252255258261264267270273276279282285288291294297306315324333342351360369378387396405414423432441450459468477486495
lin. bounds357911141517-1818-192122-2424-262728-3030-3232-3433-3636-3738-3939-4242-4444-4546-4848-5051-5253-5454-5655-5857-6059-6261-6363-6665-6866-7069-7271-7472-7675-7876-8078-8181-8483-8685-8887-9090-9290-9393-9695-9896-10098-102100-104102-106105-108107-110108-112110-114112-116114-118116-120117-122120-124122-126125-128126-130127-132129-135132-135135-138135-140138-142140-144143-146144-148146-150148-153150-154153-156153-158
best246810121515182022242627293133363739424345484851545457596063646668707274767881828486889093939698100102105105108109111114115117120122124126127129132132135137139141144144148149153153156157159162162165166168171173175177180180183186187189189195201207216222225231240243252255261270276282288291297303309315
Z27-3+1+1+1+1+19181827364554545463637281819099108108108117126126135144153162162162171180180189198198207216216225234243243243252261261270279288288297
Z27-3+2+1+1+19181827363945545463727281909099108108117120126135138147153159162171174180189189198207207216222228234243243252255261270276279288297297306
Z27-3+2+2+19121827333645485460667278849096102108114120126132138144153156162168174180186192198204207216219225234237243252255261270273279288291297306309
Z27-3+3+1+19181827363645545463727281879099105108117123126135141147153159162171174180189192198207210216225231234243246252261264270279282288294300306312
Z27-3+3+2612182430364245546066727881909399108114120126132135141147153162168171177186189195201207216222225231240243252255261270276282288291297303309315
Z3[X]/(X^2)-2+1+1+1+1+1+1366991215181818212424273030333636393942454548485154545760606363666969727575788181848787909093969699102102105108108111111114117117120123123126129129132135135138141141144144147150150153156156159162162165168168171174174177180
Z3[X]/(X^2)-2+2+1+1+1+136691215181818212124272730333336363942424548485153545760606363666969727576788181848787909293969899102105105108110111114115117120121123126126129132133135137139141144144147150150153155156159161162165167168171172174177177180183184
Z3[X]/(X^2)-2+2+2+1+1366912121518182022242627303333363839424545484951545557606163666769727275777881828487899093949699100102105106108110112114116118120122123126128129132134135138140141144145147150151153156157159162163165168169171173175177179180183185186
Z3[X]/(X^2)-2+2+2+2246810121515182021242627293133363739424345484851545457596063646668707274767881828486889093939698100102105105108109111114115117120121123126127129132132135137139141144144148149153153156157159162162165166168171173175177180180183184186189
Z3[X]/(X^3)-3+1+1+1+1+19181827364554545463637281819099108108108117126126135144153162162162171180180189198198207216216225234243243243252261261270279288297297
Z3[X]/(X^3)-3+2+1+1+19181827363945545463727281909099108108117120126135138147153159162171174180189189198207207216222228234243243252255261270276279288297297306
Z3[X]/(X^3)-3+2+2+19121827333645485460667278849096102108114120126132138144153156162168174180186192198204207216219225234237243252255261270273279288291297303309
Z3[X]/(X^3)-3+3+1+19181827363645545463727281879099105108117123126135141147153159162171177180189192198207210216225228234243246252261264270279282288294300306312
Z3[X]/(X^3)-3+3+2612182430364245546066727881909399108114120126129135141147153162168171180186189195201207216219225231237243249255261270273282288291297303309315
Z9-2+1+1+1+1+1+1366991215181818212424273030333636393942454548485154545760606363666969727578788181848787909093969699102102105108108111111114117117120123123126129129132135135138141141144144147150150153156156159162162165168168171174174177180
Z9-2+2+1+1+1+136691215181818212124272730333336363942424548485153545760606363666969727576788181848787909293969899102105105108110111114115117120121123126126129132133135137139141144144147150150153155156159161162165167168171172174177177180183184
Z9-2+2+2+1+1366912121518182022242627303333363839424545484951545557606063656769717275777881838487889093949699100102105106108110112114116117120122123126128129132134135138140141144145147150151153156157159162163165167169171173175177179180183185186
Z9-2+2+2+224681012151518202224262729313335373842424547485154545759606364666870727476788081848688909293969799102103105108109111113115117120122124126126129132132135137139141144144147149151153156156159162162165166168171172174177177180183186187189
Z9[X]/(X^2+3,X^3)-3+1+1+1+1+19181827364554545463637281819099108108108117126126135144153162162162171180180189198198207216216225234243243243252261261270279288288297
Z9[X]/(X^2+3,X^3)-3+2+1+1+19181827363945545463727281909099108108117120126135138147153159162171174180189189198207207216222228234243243252255261270276279288297297306
Z9[X]/(X^2+3,X^3)-3+2+2+19121827333645485460667278849096102108114120126132138144153156162168174180186192198204207216219225234237243252255261270273279288291297303309
Z9[X]/(X^2+3,X^3)-3+3+1+19181827363645545463727281879099105108117123126135141147153159162171177180189192198207210216225228234243246252261264270279282288294300306312
Z9[X]/(X^2+3,X^3)-3+3+2612182430364245546066727881909399108114120126129135141147153162168171180186189195201207216219225231237243249255261270273282288291297303309315
Z9[X]/(X^2+6,X^3)-3+1+1+1+1+19181827364554545463637281819099108108108117126126135144153162162162171180180189198198207216216225234243243243252261261270279288297297
Z9[X]/(X^2+6,X^3)-3+2+1+1+19181827363945545463727281909099108108117120126135138147153159162171174180189189198207207216222228234243243252255261270276279288297297306
Z9[X]/(X^2+6,X^3)-3+2+2+19121827333645485460667278849096102108114120126132138144153156162168174180186192198204207216219225234237243252255261270273279288291297303309
Z9[X]/(X^2+6,X^3)-3+3+1+19181827363645545463727281879099105108117123126135141147153159162171177180189192198207210216225228234243246252261264270279282288294300306312
Z9[X]/(X^2+6,X^3)-3+3+2612182430364245546066727881909399108114120126129135141147153162168171180186189195201207216219225231237243249255261270273282288291297303309315

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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