Results 31 to 40 of about 35,366 (273)
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 +4 more
doaj +1 more source
Twisted Reed-Solomon Codes [PDF]
, 2017 We present a new general construction of MDS codes over a finite field $\mathbb{F}_q$. We describe two explicit subclasses which contain new MDS codes of length at least $q/2$ for all values of $q \ge 11$. Moreover, we show that most of the new codes are
Beelen, Peter +2 more
core +2 more sources
Partial MDS Codes with Local Regeneration
, 2020 Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure codes that combine locality with strong erasure correction capabilities. We construct PMDS and SD codes where each local code is a bandwidth-optimal regenerating MDS code.
Holzbaur, Lukas +3 more
core +1 more source
Maximum Distance Separable Codes for Symbol-Pair Read Channels [PDF]
, 2013 We study (symbol-pair) codes for symbol-pair read channels introduced recently by Cassuto and Blaum (2010). A Singleton-type bound on symbol-pair codes is established and infinite families of optimal symbol-pair codes are constructed.
Chengmin Wang +5 more
core +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
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 +5 more
doaj +1 more source
Applications of Constacyclic Codes to Some New Entanglement-Assisted Quantum MDS Codes
IEEE Access, 2019 Generally, it is not easy to construct quantum maximal-distance-separable (MDS) codes with the minimum distance greater than $\frac {q}{2}+1$ . The minimum distance of quantum MDS codes can achieve $\frac {q}{2}+1$ or exceed $\frac {q}{2}+1$ by ...
Jianzhang Chen +5 more
doaj +1 more source
Quantum generalized Reed-Solomon codes: Unified framework for quantum MDS codes
, 2008 We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them analytically. We
F. J. MacWilliams +5 more
core +1 more source
Long MDS Codes for Optimal Repair Bandwidth [PDF]
, 2012 MDS codes are erasure-correcting codes that can correct the maximum number of erasures given the number of redundancy or parity symbols. If an MDS code has r parities and no more than r erasures occur, then by transmitting all the remaining data in ...
Bruck, Jehoshua +2 more
core +3 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 +3 more
openaire +2 more sources