The 40 cap in AG(4,4).

For more information see The largest cap in AG(4,4) and its uniqueness.

1000120212121203012302200132121213021100
0100103301231133001101230123113300330123
0010011122223333000022222222333311112222
0000000000000000111111112222222233333333
1111111111111111111111111111111111111111

The prime polynomial used to generate GF(4) is: X2+X+1. The element f=aX+b, a,b in {0,1}, is written as the number a*2+b.

The weight distribution:

A'0= 1, A'24= 15, A'28= 360, A'30= 480, A'32= 45, A'36= 120, A'40= 3.

A0= 1, A4= 8850, A5= 155520, A6= 2715720, A7= 39830400, A8= 493030665, A9= 5254640640, A10= 48883854144, A11= 399921177600, A12= 2899518786360, A13= 18735163077120, A14= 108396507811680, A15= 563661954986496, A16= 2642164808406210, A17= 11190345416616960, A18= 42896325426048960, A19= 149008283301288960, A20= 469376107672743180, A21= 1341074553869794560, A22= 3474602324145837360, A23= 8157761902302946560, A24= 17335244066991616410, A25= 33283668663994199040, A26= 57606349534835417280, A27= 89609877026460564480, A28= 124813757508016233720, A29= 154941215821597094400, A30= 170435337864502445664, A31= 164937423331478376960, A32= 139165951226845581405, A33= 101211600722039239680, A34= 62513047586763063360, A35= 32149567298243478528, A36= 13395653050888599090, A37= 4344536122264567680, A38= 1028969081983559880, A39= 158302935647802240, A40= 11872720175705661.

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