Minimum weights of the Gray images for q = 4 and size = 4^7:


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.

n162024283236404448525660646872768084889296100104108112116120124128132136140144148152156160164168172176180184188192196200204208212216220224228232236240244248252256260264268272276280284288292296300304308312316320324328332336340344348352356360364368372376380384388392396
lin. bounds810131619-2022-2324-2627-2931-3233-3536-38404446-4748-505254-5656-5960-6262-6464-6868-7171-7474-7676-8080-8382-8586-8888-9192-9494-9797-100100-103103-107106-110109-112112-115115-118118-121120-124124-127127-130130-133132-136136-140139-143141-146144-149148-152150-156153-159156-160160-164162-167166-170169-173173-176176-179180-182184-185188
best468121618222428313336404344485256566064666972767880848889929699101104108112113116120123126128131134137140144147149152156159161164167169173176180184188190192193196200203206208212215217220224227229232236240244244248250253256259262265268271273277280284288
F4[X,F]/(X^2)-2+1+1+1+1+148812162024242828323636404444485256566064646872767680848488929696100104104108112112116120124124128132136136140144144148152156156160164168168172176176180184188188192196200200204208212212216220220224228232232236240244244248252256256260264264268272
F4[X,F]/(X^2)-2+2+1+1+1488121620242428323236404044485252566060646872727680848488929496100104104108112116118120124128128132136139140144148152152156160161164168172172176180184184188192196196200204207208212216217220224228230232236240241244248252254256260264264268272276276280
F4[X,F]/(X^2)-2+2+2+1468121618222428313336404344485256566064666972767780848889929699101104108112113116120123126128131134137140144146149152156159161164167169172176179184188190192193196200202206208212214217220224226228232236238244244247249252256259262264268271273276280282288
F4[X]/(X^2)-2+1+1+1+1+148812162024242828323636404444485256566064646872767680848488929696100104104108112112116120124124128132136136140144144148152156156160164168168172176176180184188188192196200200204208212212216220220224228232232236240244244248252256256260264264268272
F4[X]/(X^2)-2+2+1+1+1488121620242428323236404044485252566060646872727680848488929296100104104108112116116120124128128132136139140144148151152156160162164168172175176180184184188192196196200204207208212216220220224228231232236240243244248252254256260264265268272276278280
F4[X]/(X^2)-2+2+2+1468121618222428313336404344485256566064666972767880848889929699101104108112113116120123126128131134137140144147148152156158161164167169172176180182185188192193196200203206208212215217220224227229232236238244244247250252256259262265268271273277280284287
GR(16,4)-2+1+1+1+1+148812162024242828323636404444485256566064646872767680848488929696100104104108112112116120124124128132136136140144144148152156156160164168168172176176180184188188192196200200204208212212216220220224228232232236240244244248252256256260264264268272
GR(16,4)-2+2+1+1+1488121620242428323236404044485252566060646872727680848488929296100104104108112116116120124128128132136139140144148151152156160162164168172175176180184184188192196196200204207208212216220220224228231232236240243244248252254256260264265268272276278280
GR(16,4)-2+2+2+1468121618222428313336404344485256566064666972767880848889929699101104108112113116120123124128131134137140144146149152156158160164167169173176180182187188192193196200202206208212214217220224226229232236240240244248250253256259262264268271273276280284287

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.

Back to main page