Minimum weights of the Gray images for q = 2 and size = 2^17:


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.

n24283236404448525660646872768084889296100104108112116120124128132136140144148152156160164168172176180184188192196200204208212216220224228232236240244248252256260264268272276280284288292296300304308312316320324328332336340344348352356360364368372376380384388392396400408416424432440448456464472480488496
lin. bounds4688-911-1212-1414-1616-1817-2020-2222-2424-2625-2827-3028-3230-3332-3633-3836-4037-4140-4340-4542-4744-4946-5148-5349-5552-5653-5856-6056-6259-6562-6664-6864-7166-7368-7670-7672-7872-8075-8278-8480-8781-8884-9087-9288-9488-9790-9992-10196-10396-10599-106101-109104-111106-112109-115112-117112-120
best244881012141618182022242628303232343638404242444648505254565860626264666870727476788082848488889092949698100102104106108108112114116118118120122124126128130132134136138140142144146148150152154154156158160162164166168170172172176180184188192196200204208212216220
Z16-4+4+4+4+188121620242432323640444852566064687276808088889296100104108112116120124128132136136144144148152156160164168172176180184188192196200204208212216220
Z2[X]/(X^3)-3+3+3+3+3+2244881012141618182022242626303232343638404242444648505254565860626264666870727476768080828488889092949698100102104106108108112112116116118120122124126128130132134136138140142144146148148150154154156158160162164166168170172
Z2[X]/(X^4)-4+4+4+4+18121620242432323640444852566064687276808084889296100104108112116120124128132136136140144148152156160164168172176180184188192196200204208212216220
Z4[X]/(X^2+2)-4+4+4+4+188121620242432323640444852566064687272768084889296100104108112116120124128132136140144144148152156160164168172176180184188192196200204208212216220
Z4[X]/(X^2+2,X^3)-3+3+3+3+3+244881012141618182022242628303232343638404242444648505254565860606264666870727476788080828486889092949698100102102104108108110114116118118120122126128130132134136138140142144146148150150152154156158160162164166168170
Z4[X]/(X^2+2X+2)-4+4+4+4+188121620242432323640444852566064687276808084889296100104108112116120124128132136136140144148152156160164168172176180184188192196200204208212216220
Z4[X]/(X^3+2,X^4)-4+4+4+4+188121620242432323640444852566064687272808084889296100104108112116120124128132136140144144148152156160164168172176180184188192196200204208212216220
Z8-3+3+3+3+3+244881012141616182022242626283232343638404242444648505254565858626264666870727476788082848486889092949698100102104106106108110114114116118120122124126128130132134136138140142144146146150152152154156158160162164166168170172

The color scheme indicates how the minimum distance of the Gray image compares to that of the best known linear codes over GF(2). It is as follows:
d There are linear codes over GF(2) with minimum distance higher than d.
d The best known linear codes over GF(2) have minimum distance d.
d It is possible that there are linear codes over GF(2) with minimum distance d or higher, but none is known yet (BTKL=better-than-known-linear).
d There are no linear codes over GF(2) with minimum distance d or higher (BTL=better-than-linear).
d There was no information about the corresponding linear codes over GF(2) in the database.

Back to main page