Determining the burst-correcting limit of cyclic codes
Hans J. Matt, J. Massey · IEEE Transactions on Information Theory · 1980
Two new computationally efficient algorithms are developed for finding the exact burst-correcting limit of a cyclic code. The first algorithm is based on testing the colmn rank of certain submatrices of the parity-check matrix of the code. An auxiliary result is a proof that every cyclic(n,k)codes with a minimum distance of at least three, corrects at least all bursts of length\lfloor (n - 2k + 1)/2 \rflooror less. The second algorithm, which requires somewhat less computation, is based on finding the length of the shortest linear feedback shift-register that generates the subsequences of lengthn - kof the sequence formed by the coefficients of the parity-check polynomialh(x), augmented with\lfloor (n-k)/2 \rfloor -1leading zeros and trailing zeros. Tables of the burst-correcting limit for a large number of binary cyclic codes are included.