On the Problem of Finding 'Sets Ensuring Linearly Independent Transversals' (SELIT), and its Application to Network Coding

摘要

This paper introduces a new formal mathematical problem initially motivated by an application of Network Coding (NC) to Information Centric Networks (ICN). It is of more limited scope but is remotely inspired by the well-known index coding problem. It is presented as follows: "given a vector space, can one construct several subsets of vectors, such that when drawing arbitrarily one vector from each subset, the selected vectors would be always linearly independent?". Answering this question is a step to construct an ICN efficient scheme with NC. We prove that our previously introduced construction is the only possible solution for a large family of constructions. This is an important result by itself. It also implies that any alternate solutions are outside this family and we propose one example.