This paper shows the existence (by construction) of rate

convolutional codes that correct bursts of length

or

random errors. The codes have memory length and guard space requirements that are asymptotically

and minimal effective length. Kohlenberg introduced the term "diffuse code" for his two random-error or single-burst error-correcting codes with minimal effective length and both a memory and guard-space requirement of

. To this point, there does not seem to be any procedure for finding codes with minimal effective length and guard space requirements asymptotically

.