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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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