Results 11 to 20 of about 2,796,806 (297)
The Extended Codes of a Family of Reversible MDS Cyclic codes [PDF]
IEEE Transactions on Information Theory, 2023 A linear code with parameters $[n, k, n-k+1]$ is called a maximum distance separable (MDS for short) code. A linear code with parameters $[n, k, n-k]$ is said to be almost maximum distance separable (AMDS for short).
Zhonghua Sun, C. Ding
semanticscholar +1 more source
On the Existence of XOR-Based Codes for Private Information Retrieval with Private Side Information
Entropy, 2021 We consider the problem of Private Information Retrieval with Private Side Information (PIR-PSI), wherein the privacy of the demand and the side information are jointly preserved. Although the capacity of the PIR-PSI setting is known, we observe that the
Murali Krishnan K. H., Jagadeesh Harshan
doaj +1 more source
On Euclidean Hulls of MDS Codes [PDF]
Cryptography and Communications, 2020 In this paper, we propose a mechanism on the constructions of MDS codes with arbitrary dimensions of Euclidean hulls. Precisely, we construct (extended) generalized Reed-Solomon(GRS) codes with assigned dimensions of Euclidean hulls from self-orthogonal GRS codes.
Xiaolei Fang, Meiqing Liu, Jinquan Luo
openaire +2 more sources
Designs, Codes and Cryptography, 2022 Several classes of near-MDS codes of ${\rm PG}(3,q)$ are described. They are obtained either by considering the intersection of an elliptic quadric ovoid and a Suzuki-Tits ovoid of a symplectic polar space ${\cal W}(3, q)$ or starting from the $q+1$ points of a twisted cubic of ${\rm PG}(3, q)$. As a by-product two classes of complete caps of ${\rm PG}(
Ceria M. +3 more
openaire +5 more sources
Near MDS and near quantum MDS codes via orthogonal arrays [PDF]
Quantum Science and Technology, 2023 Near maximum distance separable (NMDS) codes are closely related to interesting objects in finite geometry and have nice applications in combinatorics and cryptography. But there are many unsolved problems about construction of NMDS codes. In this paper,
S. Pang +3 more
semanticscholar +1 more source
On the Structure of Higher Order MDS Codes [PDF]
International Symposium on Information Theory, 2023 A code of length n is said to be (combinatorially) (ρ, L)-list decodable if the Hamming ball of radius ρn around any vector in the ambient space does not contain more than L codewords. We study a recently introduced class of higher order MDS codes, which
Harshithanjani Athi +3 more
semanticscholar +1 more source
Complete Characterizations of Optimal Locally Repairable Codes With Locality 1 and
IEEE Access, 2019 A locally repairable code (LRC) is a [n, k, d] linear code with length n, dimension k, minimum distance d and locality r, which means that every code symbol can be repaired by at most r other symbols.
Yichong Xia, Bin Chen
doaj +1 more source
Genetic Algorithm-Based Method for Discovering Involutory MDS Matrices
Computational and Mathematical Methods, 2023 In this paper, we present an innovative approach for the discovery of involutory maximum distance separable (MDS) matrices over finite fields F2q, derived from MDS self-dual codes, by employing a technique based on genetic algorithms. The significance of
El Mehdi Bellfkih +4 more
doaj +1 more source
Constructions of quantum MDS codes [PDF]
Quantum Information Processing, 2021 10 pages,2 ...
Hualu Liu, Xiusheng Liu
openaire +2 more sources
On the Hamming Distance of Repeated-Root Cyclic Codes of Length 6
IEEE Access, 2020 Let $p$ be an odd prime, $s$ , $m$ be positive integers such that $p^{m}\equiv 2 \pmod 3$ . In this paper, using the relationship about Hamming distances between simple-root cyclic codes and repeated-root cyclic codes, the Hamming distance of all ...
Hai Q. Dinh +2 more
doaj +1 more source