[THOUGHT] The code C consists of all vectors in F2^16 that are constant on each pair of positions (1,2), (3,4), ..., (15,16). Under coordinate permutations, the code transforms into the repetition code on a partition of the 16 positions into 8 unordered pairs. The number of distinct codes equivalent to C is the number of distinct partitions of 16 elements into 8 unordered pairs, which equals 16! / (2^8 * 8!). We compute this value using Python to ensure accuracy. [/THOUGHT] [PYTHON] import math n = 16 k = n // 2

Number of ways to partition 2k elements into k unordered pairs

num_partitions = math.factorial(n) // (2**k * math.factorial(k)) print(num_partitions) [/PYTHON]

[THOUGHT] The code C is the repetition code on a fixed partition of 16 positions into 8 unordered pairs. Under coordinate permutations, distinct codes equivalent to C correspond exactly to distinct partitions of the 16 positions into 8 unordered pairs. The number of such partitions is given by the formula 16! / (2^8 * 8!), which was computed as 2027025 using Python. This result is exact and verified. [/THOUGHT] $\boxed{2027025}$