Results 31 to 40 of about 35,611 (258)

On the Classification of MDS Codes [PDF]

IEEE Transactions on Information Theory, 2015
Submitted to IEEE transactions on Information Theory; presented in part at the 4th International Castle Meeting in Coding Theory and Applications, Palmela, Portugal, September ...
Krotov, Denis S., Östergård, Patric, R.J., Kokkala, Janne I.   +3 more
openaire   +3 more sources

Some New Classes of Entanglement-Assisted Quantum MDS Codes Derived From Constacyclic Codes

IEEE Access, 2019
Although quantum maximal-distance-separable (MDS) codes that satisfy the quantum singleton bound have become an important research topic in the quantum coding theory, it is not an easy task to search for quantum MDS codes with the minimum distance that ...
Jianzhang Chen, Youqin Chen, Chunhui Feng, Yuanyuan Huang, Riqing Chen   +4 more
doaj   +1 more source

On Symbol-Triple Distance of a Class of Constacyclic Codes of Length 3p^s Over F_p^m + uF_p^m

IEEE Access, 2023
Let $p\not =3$ be any prime. In this paper, we completely determine symbol-triple distance of all $\gamma $ -constacyclic codes of length $3p^{s}$ over the finite commutative chain ring ${\mathcal{ R}}=\mathbb F_{p^{m}}+u\mathbb F_{p^{m}}$ , where
Hai Q. Dinh, Bac T. Nguyen, Hiep T. Luu, Woraphon Yamaka   +3 more
doaj   +1 more source

Complete Characterizations of Optimal Locally Repairable Codes With Locality 1 and $K-1$

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

Explicit MDS Codes with Complementary Duals [PDF]

, 2017
In 1964, Massey introduced a class of codes with complementary duals which are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD codes have applications in communication system, side-channel attack (SCA) and so on. LCD codes have
Beelen, Peter, Jin, Lingfei
core   +2 more sources

Infinite families of MDS and almost MDS codes from BCH codes

, 2023
In this paper, the sufficient and necessary condition for the minimum distance of the BCH codes over $\mathbb{F}_q$ with length $q+1$ and designed distance 3 to be 3 and 4 are provided. Let $d$ be the minimum distance of the BCH code $\mathcal{C}_{(q,q+1,3,h)}$. We prove that (1) for any $q$, $d=3$ if and only if $\gcd(2h+1,q+1)>1$; (2) for $q$ odd,
Xu, Haojie, Wu, Xia, Lu, Wei, Cao, Xiwang   +3 more
openaire   +2 more sources

Zigzag Codes: MDS Array Codes With Optimal Rebuilding [PDF]

IEEE Transactions on Information Theory, 2013
23 pages, 5 figures, submitted to IEEE transactions on information ...
Tamo, Itzhak, Wang, Zhiying, Bruck, Jehoshua   +2 more
openaire   +3 more sources

Construction of reversible MDS codes in the Rosenbloom-Tsfasman metric

AIMS Mathematics
Maximum distance separable (MDS) codes are a type of error-correcting codes that aim to optimize the shortest possible distance between codewords.
Bodigiri Sai Gopinadh, Venkatrajam Marka
doaj   +1 more source

MDS Symbol-Pair Repeated-Root Constacylic Codes of Prime Power Lengths Over $\mathbb F_{p^m}+ u \mathbb F_{p^m}$

IEEE Access, 2019
MDS codes have the highest possible error-detecting and error-correcting capability among codes of given length and size. Let p be any prime, and s, m be positive integers.
H. Q. Dinh, P. Kumam, P. Kumar, S. Satpati, A. K. Singh, W. Yamaka   +5 more
doaj   +1 more source

Asymmetry Helps: Improved Private Information Retrieval Protocols for Distributed Storage [PDF]

, 2018
We consider private information retrieval (PIR) for distributed storage systems (DSSs) with noncolluding nodes where data is stored using a non maximum distance separable (MDS) linear code.
Amat, Alexandre Graell i, Kumar, Siddhartha, Lin, Hsuan-Yin, Rosnes, Eirik   +3 more
core   +2 more sources