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


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.

n1520253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195200205210215220225230235240245250255260265270275280285290295300305310315320325330335340345350355360365370375380385390395400405410415420425430435440445450455460465470475480485490495
lin. bounds9131720-2124-2529-3032-333740-4144-4549-5052-545760-616569-7072-7476-7880-828588-9092-9497-98100-101
best510151620252933374045505458606570747882869095100102106110115119120125130133137141145150154158162165170175179182186190195199202206210215219222226230235239241245250255258262266270275279282286290295300302305310315319322326330335339342346350355359362366370375379382386390
Z25-2+1+1+15101515202530354040455055556065707580859095100100100105110115120120125130135135140145150150155160165170175175180185190195195200205210215215220225230235235240245250255260262266270275280282286290295298300305310315316320325330335336340345350355360360365375375380385390
Z25-2+2+1510151620252933374045505458606570747882869095100102106110115119120125130133137141145150154158162165170175179182186190195199202206210215219222226230235239241245250255258262266270275279282286290295300302305310315319322326330335339342346350355359362366370375379382386390
Z5[X]/(X^2)-2+1+1+15101515202530354040455055556065707580859095100100100105110115120120125130135135140145150150155160165170175175180185190195195200205210212215220225230235235240245250255260260266270275280282286290295298300305310315316320325330335336340345350355360360365375375380385390
Z5[X]/(X^2)-2+2+1510151620252933374045505458606570747882869095100102106110115119120125130133137141145150154158162165170175179182186190195199202206210215219222226230235239241245250255258262266270275279282286290295300302305310315319322326330335339342346350355359362366370375379382386390

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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