We obtain a characterization on self-orthogonality for a given binary linear code in terms of the number of column vectors in its generator matrix, which extends the result of Bouyukliev et al. (2006). As an application, we give an algorithmic method to embed a given binary k-dimensional linear codeC( k = 3,4) into a self-orthogonal code of the shortest length which has the same dimension k and minimum distance d' ≥ d(C). For k > 4, we suggest a recursive method to embed a k-dimensional linear code to a self-orthogonal code. We also give new explicit formulas for the minimum distances of optimal self-orthogonal codes for any length n with dimension 4 and any length n \not ≡ 6, 13,14,21,22,28,29 (mod 31) with dimension 5.

Network lifetime maximization is an important problem particularly for large-scale wireless sensor networks. To this end, we take an approach that exploits the `sink mobility'. The sensor nodes near the sink node tend to suffer high energy consumption due to heavy traffic relay operations. As the sink node moves around, such energy bottleneck can be alleviated. We analyze the optimal sink mobility pattern obtained by solving a linear programming model and use the insights from the analysis to design a simple practical heuristic. Our heuristic utilizes only local information, e.g., the standard deviation of residual energy of neighboring sensor nodes. The simulation results show that our scheme achieves near-optimal performance even with the slowly moving mobile sink.