Hamming distance + Hamming graph small project using C++ or Java, with report.
Budget: $20 – $120 USD
Hello, I want someone to implement the below project using C++ or Java, which explains:
1: The Hamming distance dist(u, v)between two binary vectors v= (v1,...,vn)and w= (w1,...,wn)is the number of indices k such that vk≠ wk. A fundamental question in coding theory is to determine the number
A(n, d) = max | { S ⊂ {0,1}n | dist(u, v) ≥ d for all distinct u, v ∈ S }|,
The maximal number of binary vectors of length n that one can find such that any two distinct vectors have a Hamming distance ≥d. For example, A(5,4) = 2.
2: The Hamming graph H(n, d)= (V, E)is the graph with 2^n vertices V given by binary strings of length n. We have (u, v) ∈ E if and only if dist(u, v) ≥ d. The number A(n, d) coincides with the size of a maximal clique in H(n,d). Find an implement "efficient" algorithms to compute the maximal clique in the Hamming graph (but note that the problem to compute maximal cliques is NP-hard).
Note: due to the NP-hard problem, you can do exact, approximate, or heuristic.
Also I need a full well-prepared report that includes the methods have applied/used, the libraries you used, the analysis of the algorithm, what programming language been used, etc.
Must be delivered within the next 5 days.
1: The Hamming distance dist(u, v)between two binary vectors v= (v1,...,vn)and w= (w1,...,wn)is the number of indices k such that vk≠ wk. A fundamental question in coding theory is to determine the number
A(n, d) = max | { S ⊂ {0,1}n | dist(u, v) ≥ d for all distinct u, v ∈ S }|,
The maximal number of binary vectors of length n that one can find such that any two distinct vectors have a Hamming distance ≥d. For example, A(5,4) = 2.
2: The Hamming graph H(n, d)= (V, E)is the graph with 2^n vertices V given by binary strings of length n. We have (u, v) ∈ E if and only if dist(u, v) ≥ d. The number A(n, d) coincides with the size of a maximal clique in H(n,d). Find an implement "efficient" algorithms to compute the maximal clique in the Hamming graph (but note that the problem to compute maximal cliques is NP-hard).
Note: due to the NP-hard problem, you can do exact, approximate, or heuristic.
Also I need a full well-prepared report that includes the methods have applied/used, the libraries you used, the analysis of the algorithm, what programming language been used, etc.
Must be delivered within the next 5 days.