(1, 3) Optimal Linear Codes on Solid Bursts

Abstract-The paper obtains a lower bound on the necessary number of parity-check digits in an (n=n1+n2, k) linear code over GF(q) that corrects all solid burst errors of length b1 or less in the first block of length n1 and all solid burst errors of length b2 or less in the second block of length n2. Further, the author studies these codes over GF(2) that are optimal in a specific sense and gives a sufficient condition for the existence of such codes. Keywords- Parity check matrix, syndromes, solid burst, optimal codes