Problem Analysis #1

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[THOUGHT] We need to compute the number of binary linear codes equivalent to C under coordinate permutations. The code C has length 16 and is generated by the matrix [I_8 | I_8], making it self-dual. The automorphism group of C is (S_2)^8 ⋊ S_8, which has order 2^8 * 8!. The symmetric group S_16 has order 16!. By the orbit-stabilizer theorem, the size of the equivalence class is 16! / (2^8 * 8!). We will use Python to compute this value. [/THOUGHT] [PYTHON] import math num = math.factorial(16) // (2**8 * math.factorial(8)) print(num) [/PYTHON]

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