Erasure-resilient codes from affine spaces

In this paper, we investigate erasure-resilient codes (ERC) coming from Steiner 2-designs with block size k which can correct up to any k erasures. In view of applications it is desirable that such a code can also correct as many erasures of higher order as possible. Our main result is that the ERC constructed from an affine space with block size q— a special Steiner 2-design—cannot only correct up to any q erasures but even up to any 2q−1 erasures except for a small set of so-called bad erasures if q is a power of some odd prime number. This gives a new family of ERC which is asymptotically optimal in view of the check bit overhead.