Minimum weights of the Gray images for q = 5 and size = 5^7:


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.

n20253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195200205210215220225230235240245250255260265270275280285290295300305310315320325330335340345350355360365370375380385390395400405410415420425430435440445450455460465470475480485490495
lin. bounds10-111518-2023-2425-2829-3133-3536-3940-4445-4849-5152-5556-5960-6364-6769-7174-7577-7980-8385-8790-919598-99
best51012152025293237404549535560656973758085909495100103107111115120123127130135140141147150155159162166170174180185187190195200202205210215218221225230233240240245250254257260265270275278280285290295299300305308312316320325329333337340345350352356360365370374377380
Z25-2+2+1+1+15101015202530303540454550556060657075758085909495100105110110115120125125130135140145145150155160160165170175180180185190195200200205210215215220225230235235240245250255255260265270270275280285290290295300305310310315320325325330335
Z25-2+2+2+151012152025293237404548535560656973758083879195100103107111115120123127130135140141147150154158162166170174179182186190194198202205210214218221225229233236240245249253257260265269273277280285289293295300304308312316320325329332335340345348352356360365367371375379
Z5[X]/(X^2)-2+1+1+1+1+1510101520253030354040455055556065657075808085909595100105110110115120125125130135140140145150155160160165170175175180185190190195200205205210215220225225230235240240245250255260260265270275275280285290290295300305310310315320325325330335340345345350355360
Z5[X]/(X^2)-2+2+1+1+15101015202530303540454550556060657075758085909495100105110110115120125125130135140145145150155160160165170175180180185190195200200205210215215220225230235235240245250255255260265270270275280285290290295300305310310315320325325330335340345345350355360365365370
Z5[X]/(X^2)-2+2+2+151012152025293237404449535560646970758085909495100103106110115120123126130135139141147150155159161165170174180185187190195200201205210215218220225230233240240245250254257260265270275278280285290295299300305308312316320325329333337340345350352356360365370374377380

The color scheme indicates how the minimum distance of the Gray image compares to that of the best known linear codes over GF(5). It is as follows:
d There are linear codes over GF(5) with minimum distance higher than d.
d The best known linear codes over GF(5) have minimum distance d.
d It is possible that there are linear codes over GF(5) with minimum distance d or higher, but none is known yet (BTKL=better-than-known-linear).
d There are no linear codes over GF(5) with minimum distance d or higher (BTL=better-than-linear).
d There was no information about the corresponding linear codes over GF(5) in the database.

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