Dense network coding computes group operations over multiaccess networks with half the classical communication cost using shared entanglement plus quantum channels, and yields measurement-device-independent quantum key growing.
Harrow, and Andreas J
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kth-order sum-free functions correspond to codimension-m subcodes of RM(n-k,n) with minimum distance 3*2^{k-1}, yielding subcodes with 1.5 times the original distance for 2≤k≤n-2 and m≤n.
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Communication Advantages from Quantum Dense Network Coding
Dense network coding computes group operations over multiaccess networks with half the classical communication cost using shared entanglement plus quantum channels, and yields measurement-device-independent quantum key growing.
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On Reed-Muller subcodes, Grassmannian partitions and sum-free functions
kth-order sum-free functions correspond to codimension-m subcodes of RM(n-k,n) with minimum distance 3*2^{k-1}, yielding subcodes with 1.5 times the original distance for 2≤k≤n-2 and m≤n.