Results 31 to 40 of about 42,243 (288)
FNT-based reed-solomon erasure codes [PDF]
, 2009 This paper presents a new construction of Maximum-Distance Separable (MDS) Reed-Solomon erasure codes based on Fermat Number Transform (FNT). Thanks to FNT, these codes support practical coding and decoding algorithms with complexity O(n log n), where n ...
Lacan, Jérôme, Soro, Alexandre
core +3 more sources
Repeated-Root Constacyclic Codes Over the Chain Ring Fpm[u]/⟨u3⟩
IEEE Access, 2020 Let Z = Fpm[u]/(u3) be the finite commutative chain ring, where p is a prime, m is a positive integer and Fpm is the finite field with pm elements. In this paper, we determine all repeated-root constacyclic codes of arbitrary lengths over Z and their ...
Tania Sidana, Anuradha Sharma
doaj +1 more source
Local Reconstruction Codes: A Class of MDS-PIR Capacity-Achieving Codes [PDF]
, 2018 We prove that a class of distance-optimal local reconstruction codes (LRCs), an important family of repair-efficient codes for distributed storage systems, achieve the maximum distance separable private information retrieval capacity for the case of ...
Amat, Alexandre Graell i +3 more
core +2 more sources
Quantum MDS and Synchronizable Codes From Cyclic and Negacyclic Codes of Length 2
IEEE Access, 2020 Let p be an odd prime, and Fp(m) is the finite field of pm elements. In this paper, all maximum distance separable (briefly, MDS) cyclic and negacyclic codes of length 2ps over Fp(m) are established.
Hai Q. Dinh +2 more
doaj +1 more source
Near MDS poset codes and distributions [PDF]
, 2010 We study $q$-ary codes with distance defined by a partial order of the coordinates of the codewords. Maximum Distance Separable (MDS) codes in the poset metric have been studied in a number of earlier works.
Barg, Alexander, Purkayastha, Punarbasu
core +1 more source
Navigation, 2023 In this article, we present the design of a new navigation message system that includes an error-correcting scheme. This design exploits the “carousel” nature of the broadcast navigation message and facilitates (i) a reduction in the time to first fix ...
Lorenzo Ortega, Charly Poulliat
doaj +1 more source
On the Concatenation of Non-Binary Random Linear Fountain Codes with Maximum Distance Separable Codes [PDF]
2011 IEEE International Conference on Communications (ICC), 2011 The performance of a novel fountain coding scheme based on maximum distance separable (MDS) codes constructed over Galois fields of order q>=2 is investigated.
F. L. Blasco, G. Liva
semanticscholar +1 more source
Direct Construction of Optimal Rotational-XOR Diffusion Primitives
IACR Transactions on Symmetric Cryptology, 2017 As a core component of SPN block cipher and hash function, diffusion layer is mainly introduced by matrices built from maximum distance separable (MDS) codes.
Zhiyuan Guo +4 more
doaj +1 more source
Three Efficient All-Erasure Decoding Methods for Blaum–Roth Codes
Entropy, 2022 Blaum–Roth Codes are binary maximum distance separable (MDS) array codes over the binary quotient ring F2[x]/(Mp(x)), where Mp(x)=1+x+⋯+xp−1, and p is a prime number.
Weijie Zhou, Hanxu Hou
doaj +1 more source
Cyclic lowest density MDS array codes [PDF]
, 2009 Three new families of lowest density maximum-distance separable (MDS) array codes are constructed, which are cyclic or quasi-cyclic. In addition to their optimal redundancy (MDS) and optimal update complexity (lowest density), the symmetry offered by the
Bruck, Jehoshua, Cassuto, Yuval
core +4 more sources