Erasure-resilient codes from affine spaces

Authors:
Meinard Müller;Masakazu Jimbo
Affiliations:
Keio University, Department of Mathematics, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan;Keio University, Department of Mathematics, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
Venue:
Discrete Applied Mathematics
Year:
2004

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Abstract

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.