Cubic Surfaces Jaap Top - Wiskunde

Problem: fix m ≥ 1, put n := 2 m − 1 and enumerate
F 2 m = {0, α 1 , α 2 , . . . , α n } .
The binary code
BCH(m) := { (a 1 , a 2 , . . . , a n ) ∈ F n 2 ; ∑ a i α i = 0 = ∑ a i α 3 i
}
.
Alternative: put F 2 m = {0} ∪ {α l ; l ∈ Z}.
Then
BCH(m) = { f = ∑ a i x i ∈ F 2 [x]/(x n − 1) ; f(α) = 0 = f(α 3 ) } .
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