Repeated Low-Density Burst Error Detecting Codes

Abstract

Abstract. The paper deals with repeated low-density burst error detecting codes with a specified weight or less. Linear codes capable of detecting such errors have been studied. Further codes capable of correcting and simultaneously detecting such errors have also been dealt with. The paper obtains lower and upper bounds on the number of parity-check digits required for such codes. An example of such a code has also been provided.

On weights of 2-repeated low-density bursts of length b(fixed)

“…He developed codes for correcting single and double adjacent errors. Fire [6] generalized the concept of adjacent errors by introducing 'burst errors'.…”

“…A burst of length b is defined as follows [6]: Definition 1.1. A burst of length b is a vector whose only nonzero components are among some b consecutive components, the first and the last of which are non-zero.…”

“…These type of errors are termed as lowdensity bursts [9]. In the view of this concept, Dass and Garg [6] obtained results for detection and detection/correction of 2-repeated low-density bursts of length b(fixed) with weight w or less (w ≤ b) and for m-repeated low-density bursts of length b(fixed) with weight w or less (w ≤ b).…”

“…Following is the definition of 2-repeated low-density bursts of length b(fixed) with weight w or less (w ≤ b) as given by Dass and Garg [6]:…”