  A new network construction method is presented for building of scalable, high
throughput, low latency networks. The method is based on the exact equivalence
discovered between the problem of maximizing network throughput (measured as
bisection bandwidth) for a large class of practically interesting Cayley graphs
and the problem of maximizing codeword distance for linear error correcting
codes. Since the latter problem belongs to a more mature research field with
large collections of optimal solutions available, a simple translation recipe
is provided for converting the existent optimal error correcting codes into
optimal throughput networks. The resulting networks, called here Long Hop
networks, require 1.5-5 times fewer switches, 2-6 times fewer internal cables
and 1.2-2 times fewer `average hops' than the best presently known networks for
the same number of ports provided and the same total throughput. These
advantage ratios increase with the network size and switch radix. Independently
interesting byproduct of the discovered equivalence is an efficient O(n*log(n))
algorithm based on Walsh-Hadamard transform for computing exact bisections of
this class of Cayley graphs (this is NP complete problem for general graphs).
