Minimum weights of the Gray images for q = 4 and size = 4^8:


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. bounds7912-1315-1618-1920-2223-2527-2829-3132-3435-3639-404344-4648-4949-5252-5555-5857-6160-6463-6766-7068-7372-7675-7977-8280-8584-8888-9190-9493-9696-9999-102100-105104-108106-111109-114112-117115-120118-123121-126124-129127-132128-135132-138136-141138-144141-147144-150147-153150-156152-159156-162159-165162-168164-171168-174172-177175-180176-183180-187
best36812161821242528323538404448505254586264677073768082868892929699102105108112114117120124124128132136137140144146148152156159160163168170173177180181184188192192196199202205208212215216220223225228232234238240244246249252256258261264267270273276280281
F4[X,F]/(X^2)-2+2+1+1+1+148812162024242828323636404444485256566064646872
F4[X,F]/(X^2)-2+2+2+1+1488121619222428283236394044484852566060646870727680828488919296100102104108112114116120123125128132134136140144146148152155157160164166169172176179180184187190192196199201204208211213216220222224228231234236240243246248252255257260264266269272276278
F4[X,F]/(X^2)-2+2+2+236812161821242528323538404448495254586264677072768082848889929699102104108112114116120124124128131134137140144146148152156159160163168169172176180181184188192192196199202205208212215216220222225228231234238240244245249252256258261264267268271274277280
F4[X]/(X^2)-2+2+1+1+1+14881216202424282832363640444448525656606464
F4[X]/(X^2)-2+2+2+1+1488121619222428283236394044485152566060646871727680828488919296100103104108111114116120123124128132134136140144146148152155157160164167169172176178181184188190192196199201204208211213216220223224228232234236240243246248252255257260264267269272276278
F4[X]/(X^2)-2+2+2+236812161821242528323538404447505254576064677072768082868892929699102104108111114116119122124128132136137140144145148152156158160163167170173176179181184188192192196199202204208212214216220222225228231234238240244246249252256258261264267270273276280281
GR(16,4)-2+2+1+1+1+148812162024242828323636404444485256566064
GR(16,4)-2+2+2+1+1488121619222428283236394044485152566060646871727680828488919296100102104108112114116120123125128132134136140144146148152155157160164167169172176179180184187190192196199202204208211213216220222225228231234236240243245248252255258260264267269272276278
GR(16,4)-2+2+2+236812161821242528323538404448505254576064677073768082868892929699102105108111114117120122124128131136137140144145148152156159160163168169172177180181184188192192196199202204208210213216220223225228232234238240244246249252256258261264267269273275280281

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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