How to find small AI-systems for antiblocking decoding

The antiblocking decoding algorithm established in Kroll and Vincenti (2010) [6] is based on the notion of an antiblocking system. It is comparable with the permutation decoding algorithm. Instead of a permutation decoding set, called a PD-set, consisting of automorphisms of the code, it uses an antiblocking system, called an AI-system, consisting of information sets.As the permutation decoding algorithm is more efficient the smaller the PD-set, so the antiblocking decoding algorithm is more effective the smaller the AI-system. Therefore, it is important for the applications to find small AI-systems.As in the case of PD-sets, there is no method that guarantees in general how to construct optimal or nearly optimal AI-systems.In this paper, we present first some general results on the existence and construction of small antiblocking systems using properties of antiblocking systems derived in Kroll and Vincenti (2008) [4]. The crucial point for the construction of antiblocking systems is a lemma, in which a recursive procedure is provided. In the second part, we apply these findings to construct small AI-systems for some codes arising from a cap of 20 points in PG(4,3).

► We provide with a recursive procedure for the construction of small antiblocking systems.
► We give some general results on the existence and construction of small antiblocking systems.
► We present small AI-systems for some codes arising from a cap of 20 points in PG(4,3).