Stopping sets of binary parity-check matrices with constant weight columns and stopping redundancy of the associated codes - Esmaeili, Morteza; Ravanmehr, Vida (Utilitas Mathematica, 2008)
The binary linear code Hm,q, m> q≥2, of length ( qm) presented by a parity-check matrix Hm q whose columns are all distinct strings of length m and Hamming weight q ≥ 2 is considered. It is shown that the stopping distance of these matrices is three. A closed-form formula for the number of stopping sets of arbitrary size associated with these parity-check matrices is given. It turns out that Hm,2q with m ≥ 3q is an optimal redundancy code, that is redundancy and stopping redundancy of this code are equal. Among the Hm,3 codes the only optimal redundancy code is H5,3. It is shown that the stopping redundancy of Hm,2q+1 is bounded above by 2m - 2.