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∑MathIntermediate

Linear Basis for XOR

A linear basis for XOR is a compact set of at most W numbers (W = number of bits) that can generate every XOR value obtainable from a multiset of numbers.

#xor basis#linear basis#gaussian elimination f2+12
∑MathIntermediate

Matrix Rank and Linear Independence

Matrix rank is the number of pivots after Gaussian elimination and equals the dimension of both the column space and the row space.

#matrix rank
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#xor basis
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+12
∑MathAdvanced

Gaussian Elimination over GF(2)

Gaussian elimination over GF(2) is ordinary Gaussian elimination where addition and subtraction are XOR and multiplication is AND.

#gaussian elimination#gf(2)#xor basis+12