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


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.

n812162024283236404448525660646872768084889296100104108112116120124128132136140144148152156160164168172176180184188192196200204208212216220224228232236240244248252256260264268272276280284288292296300304308312316320324328332336340344348352356360364368372376380384388392396
lin. bounds47111316202225283235374044485053566063646871747680838689929698101104108111113116120123126128131134137140144146149152156159161164168171174176180183186189192
best3691216182224283135374044485053566060646770737680838688929698101104108110113116120121124128131134137140144146149152156158161164168170173176180182185188192194197200204206209212216218221224228230233236240243246249252256257260264267270272276279281284288291294297
F4[X,F]/(X^2)-2+1+148121616202424283236404448484852566064646872757880848892969699102105108112113116120124126128132136140144144148150153156160163166169172176179182185188192192196200204206208212216217220224228230233236240243246249252256256260264267270272276279281284288291294297
F4[X,F]/(X^2)-2+23691216182224283135374044485053566060646770737680838688929698101104108110113116120121124128131134137140144146149152156158161164168170173176180182185188192194197200204206209212216218221224228230233236240243246249252256257260264266269272276278281284288291294297
F4[X]/(X^2)-2+1+148121616202424283236404448484852566064646872757880848892969699102105108112113116120124126128132136140144144148150153156160163166169172176179182185188192192196200204206208212216217220224228230233236240243246249252256256260264267270272276279281284288291294297
F4[X]/(X^2)-2+23691216182224283135374044485053566060646770737680838688929698101104108110113116120121124128131134137140144146149152156158161164168170173176180182185188192194197200204206209212216218221224228230233236240243246249252256257260264266269272276278281284288291294297
GR(16,4)-2+1+148121616202424283236404448484852566064646872757880848892969699102105108112113116120124126128132136140144144148150153156160163166169172176179182185188192192196200204206208212216217220224228230233236240243246249252256256260264267270272276279281284288291294297
GR(16,4)-2+23691216182224283135374044485053566060646770737680838688929698101104108110113116120121124128131134137140144146149152156158161164168170173176180182185188192194197200204206209212216218221224228230233236240243246249252256257260264266269272276278281284288291294297

The color scheme indicates how the minimum distance of the Gray image compares to that of the best known linear codes over GF(4). It is as follows:
d There are linear codes over GF(4) with minimum distance higher than d.
d The best known linear codes over GF(4) have minimum distance d.
d It is possible that there are linear codes over GF(4) with minimum distance d or higher, but none is known yet (BTKL=better-than-known-linear).
d There are no linear codes over GF(4) with minimum distance d or higher (BTL=better-than-linear).
d There was no information about the corresponding linear codes over GF(4) in the database.

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