Minimum weights of the Gray images for q = 3 and size = 3^7:


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. bounds46810121516182021-222425-2727-283031-3333-353637-3939-4141-4243-4545-464851535455-5757-596062-63646669717273-7575-7778-7980-8181-8383-8485-8788-899091-9393-949698-9999-101101-103103-105105-107108108-111111-113113-115115-117117-119119-121121-123124-125126-127126-129129-131131-133133-135135-137137-139139-141141-144144-145144-147147-150149-151151-153153-155154-157156-159
best3469111215181821222427293032343639414245474851545456586062646668707274767881828486879092949699100102105108108110112114116117120121123126127130132135135138141142144146148150153154156159162162163165168169171174175177180182183186189190192195201207213219225231234243249252261267273279285291297303309315324
Z27-3+1+1+1+191818273645545454637281819099108108108117126135135144153162162162171180189189198207216216216225234243243252261270270270279288297303309315
Z27-3+2+1+19181827363945545463727281909399108108117126132138144153159162162171180180189198201207216216225234234243249255261270270279288294300306315324
Z27-3+2+2612182430364545546066727884909699108114120126132138144147162162168174180186192198204207216222228234240246252258264270276282288294303306315324
Z27-3+3+19121827333645485460667281879099105111114123129135141147153159165171177183189195201207213219225231234243249252261267273279285291297303309315324
Z3[X]/(X^2)-2+1+1+1+1+136691215181818212124272730333636363942424548515454545760636366667272727578818181848787909396999999102105108108111114114117117120123126126126129132132135138141144144144147150150153156159162162162165168171171174177180180180183186
Z3[X]/(X^2)-2+2+1+1+1366912131518182124242730303336363940424546485154545758606363666969727476788181848787909294969999102105105108110112114117118120123123126128130132135135138141141144146148150152154156158159162164165168170171174176177180182184186188189
Z3[X]/(X^2)-2+2+2+1346911121518182122242729303234363941424547485154545658606264666869727475788081848687909294969899102105108108110112114116117120121123126127130132133135138141142144146148150153154156159162162163165168169171174175177180182183186188189192
Z3[X]/(X^3)-3+1+1+1+191818273645545454637281819099108108108117126135135144153162162162171180189189198207216216216225234243243252261270270270279288297303309315
Z3[X]/(X^3)-3+2+1+19181827363945545463727281909399108108117126132138144153159162162171180180189198201207216216225234234243249255261270270279288294300306315324
Z3[X]/(X^3)-3+2+2612182430364545546066727884909699108114120126132138144147153162168174180186192198204207216222228234240246252258264270276282288294303306315324
Z3[X]/(X^3)-3+3+19121827333645485460667281879099105111114123129135141147153159165171177183189195201207213219225231234243249252261267273279285291297303309315324
Z9-2+1+1+1+1+136691215181818212124272730333636363942424548515454545760636366667272727578818181848787909396999999102105108108111114114117117120123126126126129132132135138141144144144147150150153156159162162162165168171171174177180180180183186
Z9-2+2+1+1+1366912131518182124242730303336363940424546485154545758606363666969727476788181848787909294969999102105105108110112114117118120123123126128130132135135138141141144146148150152154156158159162164165168170171174176177180182184186188189
Z9-2+2+2+13469111215181821222427293032343639404245464851545456586062646668707274767881828486879092949699100102105108108109111114116117120121123126127129132135135138141142144146147150153153156159162162163165168169171174175177180181183186189190192
Z9[X]/(X^2+3,X^3)-3+1+1+1+191818273645545454637281819099108108108117126135135144153162162162171180189189198207216216216225234243243252261270270270279288297303309315
Z9[X]/(X^2+3,X^3)-3+2+1+19181827363945545463727281909399108108117126132138144153159162162171180180189198201207216216225234234243249255261270270279288294300306315324
Z9[X]/(X^2+3,X^3)-3+2+2612182430364545546066727884909699108114120126132138144147153162168174180186192198204207216222228234240246252258264270276282288294303306315324
Z9[X]/(X^2+3,X^3)-3+3+19121827333645485460667281879099105111114123129135141147153159165171177183189195201207213219225231234243249252261267273279285291297303309315324
Z9[X]/(X^2+6,X^3)-3+1+1+1+191818273645545454637281819099108108108117126135135144153162162162171180189189198207216216216225234243243252261270270270279288297303309315
Z9[X]/(X^2+6,X^3)-3+2+1+19181827363945545463727281909399108108117126132138144153159162162171180180189198201207216216225234234243249255261270270279288294300306315324
Z9[X]/(X^2+6,X^3)-3+2+2612182430364545546066727884909699108114120126132138144147153162168174180186192198204207216222228234240246252258264270276282288294303306315324
Z9[X]/(X^2+6,X^3)-3+3+19121827333645485460667281879099105111114123129135141147153159165171177183189195201207213219225231234243249252261267273279285291297303309315324

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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