Error-correcting codes for list decoding

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<1/2 of the bits in an n-bit linear block code cannot prevent reliable communication at a positive rate using list-of- L decoding for sufficiently large n and an L⩽n. The new bounds are stronger for small n , but weaker for fixed e/n in the limit of large n and L than known random coding bounds