JEST2020

Question

For two n-bit strings x, y ∈ {0, 1}n, define z := x ⊕ y to be the bitwise XOR of the two strings (that is, if xi, yi, zi denote the i-th bits of x, y, z respectively, then zi = xi + yi mod 2). A function h : {0, 1}n → {0, 1}n is called linear if h(x ⊕ y) = h(x) ⊕ h(y), for every x, y ∈ {0, 1}n. The number of such linear functions for n ≥ 2:

 

1. 2^n
2. 2^2n
3. 2^(n+1)
4. n

Comments

TIFR given $2^{n^{2}}$ in 2018 as the answer

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Duplicate: https://gateoverflow.in/179294/tifr2018-b-10