Minimum weights of the Gray images for q = 3 and size = 3^5:


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.

n9121518212427303336394245485154576063666972757881848790939699102105108111114117120123126129132135138141144147150153156159162165168171174177180183186189192195198201204207210213216219222225228231234237240243246249252255258261264267270273276279282285288291294297306315324333342351360369378387396405414423432441450459468477486495
lin. bounds468101214161820222426283032353638404245464851545457596063656769727375788081828487899093949699101103105108108111113115117119121123126127129132134135137139141144145147150152153156158160162
best3469111215181821242427303033363739424345485154545557606363666972727375787981848587909193969999102105108108109111114115117120123126126128130132135136138141144144146148150153155157159162162164166168171173174177180180182184186189191192195198201207216219225234237243252255261270273279288291297306309315324327
Z27-3+1+191818273645545454637275819099108108114120126135141147153162162171177180189195201207216216225231234243249255261270270279285288297303309315324324
Z27-3+26121824333645545460667278879099108111117123129135141147153162165171180183189198201207216219225234237243252255261270273279288291297306309315324327
Z3[X]/(X^2)-2+1+1+136691215181818212427273033363636394245485154545455576062636669727274777881818487909093939699102105108108108111113114117119121123126126129131132135137139141144146148150153156159162162162165167168171173175177180180183185186189191193195
Z3[X]/(X^2)-2+2+13469111215181821242427303033363739424345485154545557606363666972727375787981848587909193969999102105108108109111114115117120123126126128130132135136138141144144146148150153155157159162162164166168171173174177180180182184186189191192195198
Z3[X]/(X^3)-3+1+191818273645545454637275819099108108114120126135141147153162162171177180189195201207216216225231234243249255261270270279285288297303309315324324
Z3[X]/(X^3)-3+26121824333645545460667278879099108111117123129135141147153162165171180183189198201207216219225234237243252255261270273279288291297306309315324327
Z9-2+1+1+136691215181818212427273033363636394245485154545455576062636669727274777881818487909093939699102105108108108111113114117119121123126126129131132135137139141144146148150153156159162162162165167168171173175177180180183185186189191193195
Z9-2+2+13469111215181821242427303033363739424345485154545557606363666972727375787981848587909193969999102105108108109111114115117120123126126128130132135136138141144144146148150153155157159162162164166168171173174177180180182184186189191192195198
Z9[X]/(X^2+3,X^3)-3+1+191818273645545454637275819099108108114120126135141147153162162171177180189195201207216216225231234243249255261270270279285288297303309315324324
Z9[X]/(X^2+3,X^3)-3+26121824333645545460667278879099108111117123129135141147153162165171180183189198201207216219225234237243252255261270273279288291297306309315324327
Z9[X]/(X^2+6,X^3)-3+1+191818273645545454637275819099108108114120126135141147153162162171177180189195201207216216225231234243249255261270270279285288297303309315324324
Z9[X]/(X^2+6,X^3)-3+26121824333645545460667278879099108111117123129135141147153162165171180183189198201207216219225234237243252255261270273279288291297306309315324327

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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