Minimum weights of the Gray images for q = 3 and size = 3^9:


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.

n1518212427303336394245485154576063666972757881848790939699102105108111114117120123126129132135138141144147150153156159162165168171174177180183186189192195198201204207210213216219222225228231234237240243246249252255258261264267270273276279282285288291294297306315324333342351360369378387396405414423432441450459468477486495
lin. bounds46910-111214-1516-171819-2121-2324-2525-2727-2929-3130-3333-3535-3636-3939-4140-4342-4545-4748-4950-5152-535454-5756-5957-6160-6361-6563-6765-6966-7169-7272-7472-7775-7977-8178-8381-8482-8684-8886-9088-9290-9492-9693-9896-10099-10299-104102-106104-108106-110108-112109-114111-115114-118115-120117-122119-124121-126123-129125-130126-132129-135131-136132-138135-141138-142141-144143-147144-148147-150149-153152-154153-157
best34681112151518202224262930313336373942424548495154545758606364666869727375787981848587909193959699101102105107108110112114117118120123124126128130132135136138141142144145148153153154156159160162163165168169171173174177180180183186189195201207213216222228234240246252258264270276282288294300306312
Z27-3+1+1+1+1+1+1918182727364554545463727281909099108108117117126135135144144153162162171180180189189198207207216225225234243243252252261270270279
Z27-3+2+1+1+1+19181827364554545463637281819099108108108117126126135144147153153162171171180189189198207207216225225234243243252261261270273279288291
Z27-3+2+2+1+1918182736364554546063727881909999108114117126132135144147153162165171180180189195201207213216225231234243246252261264270279282288297297
Z27-3+2+2+2612182430364545545766727581879399105108114120126135138144150156162168174180186189198201207216219225231237243249255261267270279282288297303
Z27-3+3+1+1+19181827363945545463727281909099105108117120126135135144153153162171174180186189198201207216222225234237243252255261270270279288291297306
Z27-3+3+2+1912182733364548546066727884909699108114120126132135144147153162165171177183189195201207213219225231237243249255261267273279285288297303309
Z27-3+3+3612182430364245545763697581879399105111117123129135141147153159165171177183189195201207213216222228234240246252258264270276282288294300306312
Z3[X]/(X^2)-2+1+1+1+1+1+1+13669912151518182124242727303333363639424245454851515454576060636366696972757578788184848790909393969999102105105108108111114114117120120123123126129129132135135138141141144144147150150153156156159162162165168168171171
Z3[X]/(X^2)-2+2+1+1+1+1+136699121518181821242427273033363639394244454848515454575760636366696972757578788184848790909396969999102105105108111111114117117120123123126128129132132135138138141144144147150150153156156159162162165168168171173174177177
Z3[X]/(X^2)-2+2+2+1+1+136691212151818182124242730313336363942424547485152545758606263666869727375787981848587909093959699100102105106108111112114117118120122123126128129132134135138139141144145147150151153156156159161162165167168171173174177178180183
Z3[X]/(X^2)-2+2+2+2+134681112151518202224262930313336373942424548495154545758606364666769727375787981848587909193959699100102105107108110112114117118120123124126128130132135136138141142144145148153153154156159160162163165168169171173174177180180183186
Z3[X]/(X^3)-3+1+1+1+1+1+1918182727364554545463727281909099108108117117126135135144144153162162171180180189189198207207216225225234243243252252261270270279
Z3[X]/(X^3)-3+2+1+1+1+19181827364554545463637281819099108108108117126126135144147153153162171171180189189198207207216225225234243243252261261270273279288291
Z3[X]/(X^3)-3+2+2+1+1918182736364554546063727881909999108114117126132135144147153162165171180180189195198207213216225231234243246252261264270279282288297300
Z3[X]/(X^3)-3+2+2+2612182430364545545763727581879399105108114120126135138144150156162168174180186189198201207216219225231237243249255261267273279282288297303
Z3[X]/(X^3)-3+3+1+1+19181827363945545463667281909099102108117120126135138144153153162168171180183189198204207216219225234240243252255261270276279288291297303
Z3[X]/(X^3)-3+3+2+1912182733364548546066727884909699108114120126132135144147153162165171180183189195201207213219225231237243249255261267273279285288297303309
Z3[X]/(X^3)-3+3+3612182430364245545763697581879399105111117123129135141147153159165171177183189195201207213216222228234240246252258264270276282288294300306312
Z9-2+1+1+1+1+1+1+13669912151518182124242727303333363639424245454851515454576060636366696972757578788184848790909393969999102105105108108111114114117120120123123126129129132135135138141141144144147150150153156156159162162165168168171171
Z9-2+2+1+1+1+1+136699121518181821242427273033363639394244454848515454575760636366696972757578788184848790909396969999102105105108111111114117117120123123126128129132132135138138141144144147150150153156156159162162165168168171173174177177
Z9-2+2+2+1+1+136691212151818182124242730313336363942424547485152545758606363666869727375787881848587899093959699100102105106108111112114116117120122123126128129132134135138139141144145147150150153155157159161162165167168171173174177178180183
Z9-2+2+2+2+134681112151518202124252930313336363941424547485154545658606263666869727375787981848587909093959699101102105107108110112114117118120122124126128129132135135138141141144145147150152153155157159162163165167168171173174177180180183185
Z9[X]/(X^2+3,X^3)-3+1+1+1+1+1+1918182727364554545463727281909099108108117117126135135144144153162162171180180189189198207207216225225234243243252252261270270279
Z9[X]/(X^2+3,X^3)-3+2+1+1+1+19181827364554545463637281819099108108108117126126135144147153153162171171180189189198207207216225225234243243252261261270273279288291
Z9[X]/(X^2+3,X^3)-3+2+2+1+1918182736364554546063727881909999108114117126132135144147153162165171180180189195198207213216225231234243246252261264270279282288297300
Z9[X]/(X^2+3,X^3)-3+2+2+2612182430364545545763727581879399105108114120126135138144150156162168174180186189198201207216219225231237243249255261267273279282288297303
Z9[X]/(X^2+3,X^3)-3+3+1+1+19181827363945545463667281909099102108117120126135138144153153162168171180183189198204207216219225234240243252255261270276279288291297303
Z9[X]/(X^2+3,X^3)-3+3+2+1912182733364548546066727884909699108114120126132135144147153162165171180183189195201207213219225231237243249255261267273279285288297303309
Z9[X]/(X^2+3,X^3)-3+3+3612182430364245545763697581879399105111117123129135141147153159165171177183189195201207213216222228234240246252258264270276282288294300306312
Z9[X]/(X^2+6,X^3)-3+1+1+1+1+1+1918182727364554545463727281909099108108117117126135135144144153162162171180180189189198207207216225225234243243252252261270270279
Z9[X]/(X^2+6,X^3)-3+2+1+1+1+19181827364554545463637281819099108108108117126126135144147153153162171171180189189198207207216225225234243243252261261270273279288291
Z9[X]/(X^2+6,X^3)-3+2+2+1+1918182736364554546063727881909999108114117126132135144147153162165171180180189195198207213216225231234243246252261264270279282288297300
Z9[X]/(X^2+6,X^3)-3+2+2+2612182430364545545763727581879399105108114120126135138144150156162168174180186189198201207216219225231237243249255261267273279282288297303
Z9[X]/(X^2+6,X^3)-3+3+1+1+19181827363945545463667281909099102108117120126135138144153153162168171180183189198204207216219225234240243252255261270276279288291297303
Z9[X]/(X^2+6,X^3)-3+3+2+1912182733364548546066727884909699108114120126132135144147153162165171180183189195201207213219225231237243249255261267273279285288297303309
Z9[X]/(X^2+6,X^3)-3+3+3612182430364245545763697581879399105111117123129135141147153159165171177183189195201204213216222228234240246252258264270276282288294300306312

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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