Lower bounds over codes correcting bursts with a given Lee weight or intensity (Q581362)

The burst error correcting and detecting capabilities of linear codes are considered. Two definitions of burst length are given. In the first, a burst of length b and Lee weight \(W_ L\) is a vector of Lee weight \(W_ L\) whose nonzero entries are confined to b consecutive positions, the first of which is nonzero. In the second a burst of length b and intensity a is a vector whose nonzero entries are confined to b consecutive positions, the first of which is nonzero and none of which has modular value exceeding a. Using combinatorial arguments, lower bounds are determined on the number of parity checks of linear codes capable of correcting bursts under the two definitions.