# Decode Reed Muller codes efficiently given only a syndrome

So given some erroneous Reed Muller code-word's syndrome as well as the Parity-Check/Generator Matrix how would one find the error vector?

The approach I took naively was to build the syndrome table, and use the syndrome to find the expected error vector, but unfortunately its too costly and for systems where $m \geq 10$, my machine definitely cannot handle it. Most decoding schemes I found require not just the syndrome but the message/erroneous code-word as well, which in this case isn't given.

Any help would be greatly appreciated.

• Describe your code more fully. What's the order and the length? – kodlu Mar 14 '18 at 6:53