2D Polynomial Code Explorer

Explore evaluation codes from polynomial spaces over Fq on the grid Fq × Fq. A message is a list of coefficients; the app evaluates the resulting polynomial on the grid and shows the codeword as numbers and pixels.

f(x,y)=Σ aᵢⱼ xⁱyʲ mod q, evaluated on all (x,y) ∈ Fq²

Monomial selection

Click cells only in custom mode. Blue = included generator monomial.

Codeword navigation

Codeword pixel object
Exact evaluation grid
Rows are x-values. Columns are y-values.
Hamming weight distribution
Highlighted red line = current codeword weight.
Total brightness distribution
Total brightness = sum of all field values in the grid.
Ready.
Generator grids
Each selected monomial produces one generator codeword. Linear combinations of these make the full code.