WebHigher-Order MDS Codes. An improved Singleton-type upper bound is presented for the list decoding radius of linear codes, in terms of the code parameters [n,k,d] and the list … WebHigher-Order MDS Codes Abstract: An improved Singleton-type upper bound is presented for the list decoding radius of linear codes, in terms of the code parameters $[n,k,d]$ …
Higher-Order MDS Codes IEEE Conference Publication IEEE …
WebHigher order MDS codes are denoted by MDS( ℓ ) where ℓ denotes the order of generality, MDS(2) codes are equivalent to the usual MDS codes. The best prior lower bound on the field size of an ( n, k )-MDS( ℓ ) codes is Ω ℓ ( n ℓ − 1 ), whereas the best known (non-explicit) upper bound is O ℓ ( n k ( ℓ − 1) ) which is exponential in the dimension. WebMaximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality. MDS self-dual codes are completely determined by the length n , so the problem of constructing q-ary MDS self-dual codes with various lengths is a very interesting topic. Recently X. Fang et al. using a … landwerks contracting
Error Decoding of Locally Repairable and Partial MDS Codes
Web21 de dez. de 2024 · Higher order MDS codes are an interesting generalization of MDS codes recently introduced by Brakensiek, Gopi and Makam (IEEE Trans. Inf. Theory … Web26 de jun. de 2024 · Higher-Order MDS Codes Abstract: An improved Singleton-type upper bound is presented for the list decoding radius of linear codes, in terms of the code parameters [n, k, d] and the list size L. L-MDS codes are then defined as codes that attain this bound (under a slightly stronger notion of list decodability), with 1 -MDS codes … Web23 de set. de 2024 · In this work it is shown that locally repairable codes (LRCs) can be list-decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error-correction capabilities. The new decoding radius is derived and the asymptotic behavior is analyzed. hemnes shoe cabinet dimensions