Results 41 to 50 of about 9,399 (155)

A Family of Almost MDS Symbol-Pair Codes of Length 8p

IEEE Access
In high-density data storage systems, symbol-pair codes are commonly used to prevent symbol-pair errors. Designing maximum distance separable (MDS) codes is crucial in symbol-pair coding theory because MDS symbol-pair codes are the best at meeting the ...
Hai Q. Dinh, Bac T. Nguyen, Hiep L. Thi, Woraphon Yamaka   +3 more
doaj   +1 more source

Constacyclic Codes of Length 3p^s Over F_p^m + uF_p^m and Their Application in Various Distance Distributions

IEEE Access, 2020
Let p ≠ 3 be any prime. The structures of all λ-constacyclic codes of length 3ps over the finite commutative chain ring Fpm + uFpm (u2 = 0) are established in the term of their generator polynomials.
Hai Q. Dinh, Bac Trong Nguyen, Woraphon Yamaka   +2 more
doaj   +1 more source

Non-restrictive MDS Array Codes for Correcting Multiple Column Erasures

Journal of King Saud University: Engineering Sciences, 2004
A new family of MDS array codes of size m × n, that we call Br (m, n, t), for correcting multiple column erasures is proposed. Br(m, n, t) codes achieve the maximum possible correcting capability, i.e., they are MDS codes with dmin = r + 1.
A.M. Al-Shahrani, A.K. Al-Jabri
doaj   +1 more source

On ℓ-MDS Codes and a Conjecture on Infinite Families of 1-MDS Codes

IEEE Transactions on Information Theory
The class of $\ell$-maximum distance separable ($\ell$-MDS) codes {is a} generalization of maximum distance separable (MDS) codes {that} has attracted a lot of attention due to its applications in several areas such as secret sharing schemes, index coding problems, informed source coding problems, and combinatorial $t$-designs. In this paper, for $\ell=
Yang Li 0194, Shixin Zhu, Edgar Martínez-Moro   +2 more
openaire   +2 more sources

Some Connections Between Classical Coding and Network Coding Over Erroneous Cyclic Networks

IEEE Access, 2016
Recently, a framework was given for linear error-correcting network codes (LENCs) over cyclic networks on commutative rings. When the alphabet is considered as a rational power series ring, an LENC is referred to as a convolutional error-correcting ...
Vahid Samadi-Khaftari, Morteza Esmaeili, Thomas Aaron Gulliver   +2 more
doaj   +1 more source

MDS Self-Dual Codes and Antiorthogonal Matrices over Galois Rings

Information, 2019
In this study, we explore maximum distance separable (MDS) self-dual codes over Galois rings G R ( p m , r ) with p ≡ − 1 ( mod 4 ) and odd r.
Sunghyu Han
doaj   +1 more source

On Group Codes Over Elementary Abelian Groups

Sultan Qaboos University Journal for Science, 2003
For group codes over elementary Abelian groups we present definitions of the generator and the parity check matrices, which are matrices over the ring of endomorphism of the group.
Adnan A. Zain
doaj   +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, Renzhang Liu, Si Gao, Wenling Wu, Dongdai Lin   +4 more
doaj   +1 more source

New Families of Asymmetric Quantum MDS Codes via Affine and Projective Partitions

Mathematics
We construct three new families of asymmetric quantum MDS codes from nested Hermitian self-orthogonal generalized Reed–Solomon and extended generalized Reed–Solomon codes over Fq2. The construction is developed in three settings: affine partitions of Fq2,
Sami H. Saif, Shayea Aldossari
doaj   +1 more source