Minimum weights of the Gray images for q = 4 and size = 4^6:


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.

n12162024283236404448525660646872768084889296100104108112116120124128132136140144148152156160164168172176180184188192196200204208212216220224228232236240244248252256260264268272276280284288292296300304308312316320324328332336340344348352356360364368372376380384388392396
lin. bounds681114172023-2426-2729-303235-3637-39414447-4850-515456-5759-6062-6364-6567-6870-7273-7576-7879-8083-8486-8788-9092-939697-99100-102104-105106-108109-112112-114116-117119-120121-124124-126127-128130-132133-135136-138139-141142-144145-147148-150152-153154-156157-160160-162163-165166-168169-172172-175176-177179-180182-184185-187188-190
best369121618222427313436404447495256606064666972757881838689929699102105108112114117120123127129131134137140144147150153156160162165168171176179181184188192192195198201204208210213216220224226229232236237240244248249252256258261264267270272275278281284288291
F4[X,F]/(X^2)-2+1+1+1+1488121620242428323236404044485256566064646872768080848888929696100104108112112116120120124128128132136140144144148152152156160164164168172176176180184188192192196200200204208212212216220224224228232232236240244244248252256256260264268268272276280280
F4[X,F]/(X^2)-2+2+1+14881216202424283234364043464852565660646870727680818488929396100104104108112116117120124128129132136138141144148152153156160164166168172176178181184188192193196200202205208212216217220224226229233236240242246249252254256260263266270272275278280284287288
F4[X,F]/(X^2)-2+2+2369121618222427313436404447485154576064666972757880838689929699102104108112114117120123127128131134137140144147150152156160162165168171176176181184188192192195198200204208210213214220223226229232236236239243245248252256258261264267268272275278281284288290
F4[X]/(X^2)-2+1+1+1+1488121620242428323236404044485256566064646872768080848888929696100104108112112116120120124128128132136140144144148152152156160164164168172176176180184188192192196200200204208212212216220224224228232232236240244244248252256256260264268268272276280280
F4[X]/(X^2)-2+2+1+14881216202424283234364043464852565660646870727680818488929396100104104108112116117120124128129132136138141144148152153156160164166168172176178181184188191193196200204205208211216217220224227229233236239241244248251254256260263266270272274278281284288288
F4[X]/(X^2)-2+2+2369121618222427313436404447485154576063666972757880838689929699102105108112114117120123126129131134137140144147150152156160162165168171175178180182188192192195198201203207210212214220223226229232236236240243246249252256257259264265268272275278281284287291
GR(16,4)-2+1+1+1+1488121620242428323236404044485256566064646872768080848888929696100104108112112116120120124128128132136140144144148152152156160164164168172176176180184188192192196200200204208212212216220224224228232232236240244244248252256256260264268268272276280280
GR(16,4)-2+2+1+14881216202424283234364043464852565660646870727680818488929396100104104108112116117120124128129132136138141144148152153156160164166168172176178181184188191193196200204205208211216217220224227229233236239241244249251254256260263266270272274278281284288288
GR(16,4)-2+2+2369121618222427313436404447495256606063666972757881838689929699102105108112114117120123126128131134137140144147150153156160162165168171176179180184188192192195198200203208210213214220224226229232236237240244248248252256257259264265268272275278280284287291

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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