On the List Decodability of Self-orthogonal Rank Metric Codes

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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 venkat2017. 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 -linear self-orthogonal rank metric code over Fqⁿ× ᵐ of rate R=(1-τ)(1-n/mτ)-ε is shown to be list decodable up to fractional radius τ∈(0,1) and small ε∈(0,1) with list size depending on τ and q at most Oτ, q(1ε). In addition, we show that an Fqₘ-linear self-orthogonal rank metric code of rate up to the Gilbert-Varshamov bound is (τn, (Oτ, q(1ε)))-list decodable.