Minimum weights of the Gray images for q = 3 and size = 3^10:


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. bounds4689-1011-1213-1415-161818-2021-2222-2424-2626-2827-3030-3231-3433-3635-3836-4039-4241-4443-4645-4848-5050-5251-5453-5654-5856-6057-6260-6461-6663-6865-7068-7271-7472-7673-7875-8078-8279-8481-8682-8884-9086-9287-9490-9692-9895-10096-10298-104100-106102-107104-109105-111108-113108-115111-117113-119114-121117-123118-125120-127123-129125-131126-134128-135131-137134-140135-141137-143140-145142-147145-149148-151151-153153-155
best2468101215151819202224272830323436373942434547485153545758606264666869727375787981838487899093949699100102104106108109111114115117120121123125126129131133135137139141143144147148151153154156158160162163165167168171173174177179180183189195201207213219225231234243246252258264270276282288294300306
Z27-3+3+1+1+1+1918182736455454545463727281909699108108117126126135144144153153162171177180189189198207207216219225234234243252258261270270279288288
Z27-3+3+2+1+1918182736364554546063727884909999108111117126129135144147153162165171174180189192198207210216225228234243246252258261270276282288294297
Z27-3+3+2+2612182430364245545766727281879099105108114120126132138144150153162168171180183189198201207213219225231237243249255261267270276282288297300
Z27-3+3+3+1912182433364248546066727884909699108114117126129135144147153159165171177183189195201207213219225231234243246252258264270276282288294300306
Z3[X]/(X^2)-2+1+1+1+1+1+1+1+1366991212151818212124242730303333363639424245454851515454576060636366696972757578788184848787909393969699102102105105105105105105105105105105105105105105105105105105105105105105105105105105105105105105105105105
Z3[X]/(X^2)-2+2+1+1+1+1+1+13669912121518182124242727303033363636394245454548515454576060636366696972727578788184848787909393969999102102105108108111114114117117120123126126129129132135135138141141144147147150150153156156159161162165168168171171
Z3[X]/(X^2)-2+2+2+1+1+1+136699121516181821242427273033333639394242454848515454575860636366696972737578788184848788909394969999102105105108111111114117117120122123126127129132132135137138141143144147149150153154156159159162165165168170171174176177
Z3[X]/(X^2)-2+2+2+2+1+13669111215151818212424272930333436373942444548495153555759606364666970727475788081848587899193959699101102105106108111112114116118120122123126128129132133135138139141143145147149150153154156159160162165166168171172174176178180
Z3[X]/(X^2)-2+2+2+2+2246810121315181920222427283031333637394142454648505254565760616365676971727476788182848688909293969799101103105107109111113114117119120123124126128130132134136138140141144146147150151153155157159161163165167168171173174177178180
Z3[X]/(X^3)-3+3+1+1+1+1918182736455454545463727281909699108108117126126135144144153153162171171180189189198207207216216225234234243252258261270270279288288
Z3[X]/(X^3)-3+3+2+1+1918182736364554546063727884909699108114117126126135144147153159162171177180189195198207210216225228234240246252258264270276282288294297
Z3[X]/(X^3)-3+3+2+2612182430364245545763727281879099105108114120126132138144150156162168171180183189198201207216219225231237243249255261267270279282288297303
Z3[X]/(X^3)-3+3+3+1912182433364248546066727884909699108114117126129135144147153159165171177183189195201207213219225231234243246252258264270276282288294300306
Z9-2+1+1+1+1+1+1+1+1366991212151818212124242730303333363639424245454851515454576060636366696972757578788184848787909393969699102102105105105105105105105105105105105105105105105105105105105105105105105105105105105105105105105105105
Z9-2+2+1+1+1+1+1+13669912121518182124242727303033363636394245454548515454576060636366696972727578788184848787909393969999102102105108108111114114117117120123126126129129132135135138141141144147147150150153156156159161162165168168171171
Z9-2+2+2+1+1+1+1366991215161818212424272730333336393942424548485154545757606363666969727375787881848487899093969699100102105105108111111114116117120121123126127129132132135138138141142144147149150153153156159159162164165168170171174176177
Z9-2+2+2+2+1+13669111215151818212424272930333436373942454548495154555759606364666970727475788081848587909193959699101102105106108110112114116118120122123126128129132133135138139141143145147149150153154156159160162164166168170172174176178180
Z9-2+2+2+2+22468101215151819202224272830323436373942434547485153545758606264666869727375787981838487899093949699100102104106108109111114115117120121123125126129131133135137139141143144147148151153154156158160162163165167168171173174177179180
Z9[X]/(X^2+3,X^3)-3+3+1+1+1+1918182736455454545463727281909699108108117126126135144144153153162171171180189189198207207216216225234234243252258261270270279288288
Z9[X]/(X^2+3,X^3)-3+3+2+1+1918182736364554546063727884909699108114117126126135144147153159162171177180189195198207210216225228234240246252258264270276282288294297
Z9[X]/(X^2+3,X^3)-3+3+2+2612182430364245545763727281879099105108114120126132138144150156162168171180183189198201207216219225231237243249255261267270279282288297303
Z9[X]/(X^2+3,X^3)-3+3+3+1912182433364248546066727884909699108114117126129135141147153159165171177183189195201207213219225231234243246252258264270276282288294300306
Z9[X]/(X^2+6,X^3)-3+3+1+1+1+1918182736455454545463727281909699108108117126126135144144153153162171171180189189198207207216216225234234243252258261270270279288288
Z9[X]/(X^2+6,X^3)-3+3+2+1+1918182736364554546063727884909699108114117126126135144147153159162171177180189195198207210216225228234240246252258264270276282288294297
Z9[X]/(X^2+6,X^3)-3+3+2+2612182430364245545763727281879099105108114120126132138144150156162168171180183189198201207216219225231237243249255261267270279282288297303
Z9[X]/(X^2+6,X^3)-3+3+3+1912182433364248546066727884909699108114117126129135141147153159165171177183189195201207213219225231234243246252258264270276282288294300306

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