On the Decoder Error Probability of Bounded Rank-Distance Decoders for Maximum Rank Distance Codes

Details On the Decoder Error Probability of Bounded Rank-Distance Decoders for Maximum Rank Distance Codes On the Decoder Error Probability of Bounded Rank-Distance Decoders for Maximum Rank Distance Codes

2006-12-08

arxiv.org/abs/cs/0612051v2

Computer Science

Information Theory

5 pages. To appear in IEEE Transactions on Information Theory

Scientific paper

In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes that parallel those of maximum distance separable codes. Using these properties, we show that, for MRD codes with error correction capability t, the decoder error probability of bounded rank distance decoders decreases exponentially with t^2 based on the assumption that all errors with the same rank are equally likely.

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