Error-correcting codes for list decoding

The authors show that a jammer who can change a fixed fraction p > indicates that the maximum rate of (n,e,L) codes, which correct all sets of e or fewer errors in a block of n bits under list-of-L decoding, is limited.

Abstract

In the list-of-L decoding of a block code the receiver of a noisy sequence lists L possible transmitted messages, and is in error only if the correct message is not on the list. Consideration is given to (n,e,L) codes, which correct all sets of e or fewer errors in a block of n bits under list-of-L decoding. New geometric relations between the number of errors corrected under list-of-1 decoding and the (larger) number corrected under list-of-L decoding of the same code lead to new lower bounds on the maximum rate of (n,e,L) codes. They show that a jammer who can change a fixed fraction p>