On the List Decodability of Self-orthogonal Rank Metric Codes

V. Guruswami and N. Resch prove that the list decodability of Fq-linear rank metric codes is as good as that of random rank metric codes in [17]. Due to the potential applications of self-orthogonal rank metric codes, we focus on list decoding of them. In this paper, we prove that with high probability, an Fq-linear self-orthogonal rank metric code over Fn×m q of rate R = (1 − τ)(1 − n mτ) − is shown to be list decodable up to fractional radius τ ∈ (0, 1) and small ∈ (0, 1) with list size depending on τ and q at most Oτ,q( 1 ). In addition, we show that an Fqm -linear self-orthogonal rank metric code of rate up to the Gilbert-Varshamov bound is (τn, exp(Oτ,q( 1 )))-list decodable.