We present below the ways in how a Cartesian code $C$ can be defined.
cartesianCode(F, L, d)
F is a field, L is a list of subsets of F and d is an integer. Returns the Cartesian code $C$ obtained when polynomials of degree at most d are evaluated over the points of the Cartesian product made by the subsets of L.
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cartesianCode(F, L, S)
F is a field, L is a list of subsets of F and S is a set of polynomials. Returns the Cartesian code $C$ obtained when polynomials in the list S are evaluated over the points of the Cartesian product made by the subsets of L.
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cartesianCode(F, L, M)
F is a field, L is a list of subsets of F and M is the matrix whose rows are the exponents of the monomials to evaluate. Returns the Cartesian code $C$ obtained when the monomials defined by the matrix M are evaluated over the points of the Cartesian product made by the subsets of L.
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While this function may work even when a ring is given, instead of a finite field, it is possible that the results are not the expected ones.
The object cartesianCode is a method function with options.