198 research outputs found
Construction algorithm for network error-correcting codes attaining the Singleton bound
We give a centralized deterministic algorithm for constructing linear network
error-correcting codes that attain the Singleton bound of network
error-correcting codes. The proposed algorithm is based on the algorithm by
Jaggi et al. We give estimates on the time complexity and the required symbol
size of the proposed algorithm. We also estimate the probability of a random
choice of local encoding vectors by all intermediate nodes giving a network
error-correcting codes attaining the Singleton bound. We also clarify the
relationship between the robust network coding and the network error-correcting
codes with known locations of errors.Comment: To appear in IEICE Trans. Fundamentals
(http://ietfec.oxfordjournals.org/), vol. E90-A, no. 9, Sept. 2007. LaTeX2e,
7 pages, using ieice.cls and pstricks.sty. Version 4 adds randomized
construction of network error-correcting codes, comparisons of the proposed
methods to the existing methods, additional explanations in the proo
Algebraic geometric construction of a quantum stabilizer code
The stabilizer code is the most general algebraic construction of quantum
error-correcting codes proposed so far. A stabilizer code can be constructed
from a self-orthogonal subspace of a symplectic space over a finite field. We
propose a construction method of such a self-orthogonal space using an
algebraic curve. By using the proposed method we construct an asymptotically
good sequence of binary stabilizer codes. As a byproduct we improve the
Ashikhmin-Litsyn-Tsfasman bound of quantum codes. The main results in this
paper can be understood without knowledge of quantum mechanics.Comment: LaTeX2e, 12 pages, 1 color figure. A decoding method was added and
several typographical errors were corrected in version 2. The description of
the decoding problem was completely wrong in version 1. In version 1 and 2,
there was a critical miscalculation in the estimation of parameters of codes,
and the constructed sequence of codes turned out to be worse than existing
ones. The asymptotically best sequence of quantum codes was added in version
3. Section 3.2 appeared in IEEE Transactions on Information Theory, vol. 48,
no. 7, pp. 2122-2124, July 200
Improved Asymptotic Key Rate of the B92 Protocol
We analyze the asymptotic key rate of the single photon B92 protocol by using
Renner's security analysis given in 2005. The new analysis shows that the B92
protocol can securely generate key at 6.5% depolarizing rate, while the
previous analyses cannot guarantee the secure key generation at 4.2%
depolarizing rate.Comment: IEEEtran.sty, 3 pages, 1 figure. Submitted to IEEE ISIT 201
Fidelity of a t-error correcting quantum code with more than t errors
It is important to study the behavior of a t-error correcting quantum code
when the number of errors is greater than t, because it is likely that there
are also small errors besides t large correctable errors. We give a lower bound
for the fidelity of a t-error correcting stabilizer code over a general
memoryless channel, allowing more than t errors. We also show that the fidelity
can be made arbitrary close to 1 by increasing the code length.Comment: 9 pages, ReVTeX4 beta 5. To be published in Phys. Rev. A. The lower
bound is made tighter in version 4 and 5. All approximations in the first
version are removed, and a lower bound for the average of the fidelity is
given in the second version. A critical error is correcte
Message Randomization and Strong Security in Quantum Stabilizer-Based Secret Sharing for Classical Secrets
We improve the flexibility in designing access structures of quantum
stabilizer-based secret sharing schemes for classical secrets, by introducing
message randomization in their encoding procedures. We generalize the
Gilbert-Varshamov bound for deterministic encoding to randomized encoding of
classical secrets. We also provide an explicit example of a ramp secret sharing
scheme with which multiple symbols in its classical secret are revealed to an
intermediate set, and justify the necessity of incorporating strong security
criterion of conventional secret sharing. Finally, we propose an explicit
construction of strongly secure ramp secret sharing scheme by quantum
stabilizers, which can support twice as large classical secrets as the
McEliece-Sarwate strongly secure ramp secret sharing scheme of the same share
size and the access structure.Comment: Publisher's Open Access PDF. arXiv admin note: text overlap with
arXiv:1811.0521
Quantum Stabilizer Codes Can Realize Access Structures Impossible by Classical Secret Sharing
We show a simple example of a secret sharing scheme encoding classical secret
to quantum shares that can realize an access structure impossible by classical
information processing with limitation on the size of each share. The example
is based on quantum stabilizer codes.Comment: LaTeX2e, 5 pages, no figure. Comments from readers are welcom
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