Prove the Singleton bound: A(n, d) ≤ 2^(n−d+1).
Analyze the prove the singleton bound: a(n, d) ≤ 2^(n−d+1)..
Examples
Input: "test_input_1"
Output: "output_1"
Input: "test_input_2"
Output: "output_2"
Hints
Recall the definition of the Hamming bound and how it relates to the number of codewords in a code with a given minimum distance.
Consider the concept of sphere packing in the context of error-correcting codes and how it limits the number of codewords that can be packed into the space without overlapping.
Examine the relationship between the minimum distance of a code and the maximum number of errors it can correct, then derive the upper bound on the number of codewords using combinatorial arguments.
Prove the Singleton bound: A(n, d) ≤ 2^(n−d+1).
Analyze the prove the singleton bound: a(n, d) ≤ 2^(n−d+1)..