On the List Decodability of Self-orthogonal Rank Metric Codes

01/22/2018

∙

by   Shu Liu, et al.

∙

0

∙

share

V. Guruswami and N. Resch prove that the list decodability of F_q-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 _q-linear self-orthogonal rank metric code over F_q^n× 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 O_τ, q(1/ϵ). In addition, we show that an F_q^m-linear self-orthogonal rank metric code of rate up to the Gilbert-Varshamov bound is (τ n, (O_τ, q(1/ϵ)))-list decodable.