In this paper, we introduce a lower bound for the generalized Hamming weights, which is applicable to arbitrary linear code, in terms of the notion of well-behaving. We also show that any [n,k] linear code C over a finite field F is the t-th rank MDS for t such that g(C)+1 t k where g(C) is easily calculated from the basis of Fn so chosen that whose first n-k elements generate C. Finally, we apply our result to Reed-Solomon, Reed-Muller and algebraic geometry codes on Cab, and determine g(C) for each code.

The relationships between producers and consumers have changed radically by the recent growth of sharing economy. Promoting resource sharing can contribute to finding a solution to environmental issues (e.g. reducing food waste, consuming surplus electricity, and so on). Although prosumers have both roles as consumers and suppliers, matching between suppliers and consumers should be determined when the prosumers share resources. Especially, it is important to achieve envy-freeness that is a metric indicating how the number of prosumers feeling unfairness is kept small since the capacity of prosumers to supply resources is limited. Changing resource capacity and demand will make the situation more complex. This paper proposes a resource sharing model based on a temporal network and flows to realize envy-free resource sharing among prosumers. Experimental results demonstrate the deviation of envy among prosumers can be reduced by setting appropriate weights in a flow network.

Higher transmission rates are one of the main characteristics of the fourth-generation (4G*) of mobile communications. These systems are expected to operate at higher frequency bands, which experience larger propagation loss. This results in larger required transmission power, which causes several problems, particularly for uplink communications, as the typical mobile station (MS) has limited transmission power. Multi-hop systems have been proposed to address this problem. In this paper, we consider the issue of random-access (RA) in a multi-hop system. It is clear that a two-hop mobile communication system requires a two-stage RA process. In this paper, we propose a two-stage RA process that is an extension of the RA process of the CDMA-based 3GPP standard. The proposed method uses a hybrid of code division multiple access (CDMA) and Slotted-ALOHA. To realize the proposed two-hop RA, we dedicate one slot for second-hop transmissions in each interval (predefined); we refer to this as the interval slots allocation (ISsA) technique. Numerical analyses and simulations are conducted to evaluate its basic performance in a multi-hop system. The results demonstrate the superior throughput-delay performance of the proposed two-stage RA multi-hop system with ISsA.

Many countries have deregulated their electricity retail markets to offer lower electricity charges to consumers. However, many consumers have not switched their suppliers after the deregulation, and electricity suppliers do not tend to reduce their charges intensely. This paper proposes an electricity market model and evolutionary game to analyze the behavior of consumers in electricity retail markets. Our model focuses on switching costs such as an effort at switching, costs in searching for other alternatives, and so on. The evolutionary game examines whether consumers choose a strategy involving exploration of new alternatives with the searching costs as “cooperators” or not. Simulation results demonstrate that the share of cooperators was not improved by simply giving rewards for cooperators as compensation for searching costs. Furthermore, the results also suggest that the degree of cooperators in a network among consumers has a vital role in increasing the share of cooperators and switching rate.