Recent advances in technology have produced a requirement for new implementations of good error-correcting codes. Such applications of codes also require efficient encoding and decoding methods.
The method of permutation decoding was first developed by Mac-Williams in the early 60's and can be used when a code has a sufficiently large automorphism group to ensure the existence of a set of automorphisms, called a PD-set, that has some specific properties.
We describe here the method, and why it works, and give a short survey of permutation decoding using codes that arise from combinatorial structures such as graphs, designs and finite geometries, including some recent results in the search for PD-sets.
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