On the separating redundancy of extended Hamming codes

Separating redundancy, proposed by Abdel-Ghaffar and Weber, is an important concept in the analysis of the error and erasure decoding of a linear block code using a parity-check matrix of the code. In this paper, we investigate the second and third separating redundancies of extended Hamming codes. For an extended Hamming code, we establish two binary integer linear program problems, the optima of which give lower and upper bounds on the second/third separating redundancy of the code. Numerical results suggest that our bounds might improve the known bounds of the second and third separating redundancies of extended Hamming codes.