Minimum weights of the Gray images for q = 3 and size = 3^4:


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.

n69121518212427303336394245485154576063666972757881848790939699102105108111114117120123126129132135138141144147150153156159162165168171174177180183186189192195198201204207210213216219222225228231234237240243246249252255258261264267270273276279282285288291294297306315324333342351360369378387396405414423432441450459468477486495
lin. bounds25691112151819212426272931333637394244454850525455576062636668707274767881818486889092949699100102105107108110112114117118120123125126129131133135136138141143144147149151153155157159162162
best24681112151819212424272931333637394243454849515455576061636667697274767881818486879092949699100102105106108110112114117118120123124126129130132135136138141142144147148150153155157159162162165167168171173175177180181183186187189191193195198199204210216222228234243246252261264270279282288297300306315318324333
Z27-3+19181827363945545763727581909399108111117126129135144147153162168174180186192198204210216222228234243246252261264270279282288297300306315318324333
Z3[X]/(X^2)-2+1+136691215181818212425273033363638404245474951545457606063666769727476788181848687909294969999102104105108110112114117117120122123126128130132135136138141142144147148150153155157159162162165167168171173175177180180183185186189191193195198198
Z3[X]/(X^2)-2+224681112151819212424272931333637394243454849515455576061636667697274767881818485879092949699100102105106108110112114117118120123124126129130132135136138141142144147148150153155157159162162165166168171173175177180181183186187189191193195198199
Z3[X]/(X^3)-3+19181827363945545763727581909399108111117126129135144147153162168174180186192198204210216222228234243246252261264270279282288297300306315318324333
Z9-2+1+136691215181818212425273033363638404245474951545457606063666769727476788181848687909294969999102104105108110112114117117120122123126128130132135136138141142144147148150153155157159162162165167168171173175177180180183185186189191193195198198
Z9-2+224681112151819212424272931333637394243454849515455576061636667697274767881818485879092949699100102105106108110112114117118120123124126129130132135136138141142144147148150153155157159162162165166168171173175177180181183186187189191193195198199
Z9[X]/(X^2+3,X^3)-3+19181827363945545763727581909399108111117126129135144147153162168174180186192198204210216222228234243246252261264270279282288297300306315318324333
Z9[X]/(X^2+6,X^3)-3+19181827363945545763727581909399108111117126129135144147153162168174180186192198204210216222228234243246252261264270279282288297300306315318324333

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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