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61.
William J. Martin 《Designs, Codes and Cryptography》2000,21(1-3):181-187
A code C F
n is s-regular provided, forevery vertex x F
n, if x is atdistance at most s from C then thenumber of codewords y C at distance ifrom x depends only on i and the distancefrom x to C. If denotesthe covering radius of C and C is -regular,then C is said to be completely regular. SupposeC is a code with minimum distance d,strength t as an orthogonal array, and dual degrees
*. We prove that d 2t + 1 whenC is completely regular (with the exception of binaryrepetition codes). The same bound holds when C is(t + 1)-regular. For unrestricted codes, we show thatd s
* + t unless C is a binary repetitioncode. 相似文献
62.
Long Gui-lu Deng Fu-guo Wang Chuan Li Xi-han Wen Kai Wang Wan-ying 《Frontiers of Physics in China》2007,2(3):251-272
In this review article, we review the recent development of quantum secure direct communication (QSDC) and deterministic secure
quantum communication (DSQC) which both are used to transmit secret message, including the criteria for QSDC, some interesting
QSDC protocols, the DSQC protocols and QSDC network, etc. The difference between these two branches of quantum communication
is that DSQC requires the two parties exchange at least one bit of classical information for reading out the message in each
qubit, and QSDC does not. They are attractive because they are deterministic, in particular, the QSDC protocol is fully quantum
mechanical. With sophisticated quantum technology in the future, the QSDC may become more and more popular. For ensuring the
safety of QSDC with single photons and quantum information sharing of single qubit in a noisy channel, a quantum privacy amplification
protocol has been proposed. It involves very simple CHC operations and reduces the information leakage to a negligible small
level. Moreover, with the one-party quantum error correction, a relation has been established between classical linear codes
and quantum one-party codes, hence it is convenient to transfer many good classical error correction codes to the quantum
world. The one-party quantum error correction codes are especially designed for quantum dense coding and related QSDC protocols
based on dense coding.
相似文献
63.
64.
We give a new exposition and proof of a generalized CSS construction for nonbinary quantum error-correcting codes. Using this we construct nonbinary quantum stabilizer codes with various lengths, dimensions, and minimum distances from algebraic curves. We also give asymptotically good nonbinary quantum codes from a Garcia–Stichtenoth tower of function fields which are constructible in polynomial time. 相似文献
65.
Chi-Kwong Li 《Journal of Mathematical Analysis and Applications》2008,348(2):843-855
For a positive integer k, the rank-k numerical range Λk(A) of an operator A acting on a Hilbert space H of dimension at least k is the set of scalars λ such that PAP=λP for some rank k orthogonal projection P. In this paper, a close connection between low rank perturbation of an operator A and Λk(A) is established. In particular, for 1?r<k it is shown that Λk(A)⊆Λk−r(A+F) for any operator F with rank(F)?r. In quantum computing, this result implies that a quantum channel with a k-dimensional error correcting code under a perturbation of rank at most r will still have a (k−r)-dimensional error correcting code. Moreover, it is shown that if A is normal or if the dimension of A is finite, then Λk(A) can be obtained as the intersection of Λk−r(A+F) for a collection of rank r operators F. Examples are given to show that the result fails if A is a general operator. The closure and the interior of the convex set Λk(A) are completely determined. Analogous results are obtained for Λ∞(A) defined as the set of scalars λ such that PAP=λP for an infinite rank orthogonal projection P. It is shown that Λ∞(A) is the intersection of all Λk(A) for k=1,2,…. If A−μI is not compact for all μ∈C, then the closure and the interior of Λ∞(A) coincide with those of the essential numerical range of A. The situation for the special case when A−μI is compact for some μ∈C is also studied. 相似文献
66.
Most of the literature on coded excitation describes the signal-to-noise ratio gain of a coded waveform in terms of the time-bandwidth product. We have shown that in the context of ultrasound imaging, the expression for the SNR gain provided by matched filtering a coded waveform, can be reduced to the total number of chips in the transmit signal. Hence, the SNR gain is independent of both the bandwidth and the duration of a single-chip. This concept is described in detail, clarifying this seeming contradiction. The impact of bandwidth and pulse duration on the SNR, SNR gain and axial resolution is described. Bandwidth requirements and the impact of regulatory peak-power limitations are also addressed. 相似文献
67.
Shigeto Nishimura 《Discrete Applied Mathematics》2008,156(12):2352-2358
In this contribution the Riemann hypothesis analogue presented by Iwan Duursma is considered. Whether the analogue for a given selfdual code holds depends on its Hamming weight enumerator. A necessary and sufficient condition is provided in the case of genus less than 3 for the homogeneous polynomials in two variables invariant under the MacWilliams transform. Also the case of half integral genus is studied and similar results are obtained. 相似文献
68.
Gennian Ge 《Discrete Mathematics》2008,308(13):2704-2708
In this note, we consider a construction for optimal ternary constant weight codes (CWCs) via Bhaskar Rao designs (BRDs). The known existence results for BRDs are employed to generate many new optimal nonlinear ternary CWCs with constant weight 4 and minimum Hamming distance 5. 相似文献
69.
This paper extends the concepts from cyclic duadic codes to negacyclic codes over Fq (q an odd prime power) of oddly even length. Generalizations of defining sets, multipliers, splittings, even-like and odd-like codes are given. Necessary and sufficient conditions are given for the existence of self-dual negacyclic codes over Fq and the existence of splittings of 2N, where N is odd. Other negacyclic codes can be extended by two coordinates in a way to create self-dual codes with familiar parameters. 相似文献
70.
Koji Nuida Satoshi Fujitsu Manabu Hagiwara Takashi Kitagawa Hajime Watanabe Kazuto Ogawa Hideki Imai 《Designs, Codes and Cryptography》2009,52(3):339-362
It has been proven that the code lengths of Tardos’s collusion-secure fingerprinting codes are of theoretically minimal order
with respect to the number of adversarial users (pirates). However, the code lengths can be further reduced as some preceding
studies have revealed. In this article we improve a recent discrete variant of Tardos’s codes, and give a security proof of
our codes under an assumption weaker than the original Marking Assumption. Our analysis shows that our codes have significantly
shorter lengths than Tardos’s codes. For example, when c = 8, our code length is about 4.94% of Tardos’s code in a practical setting and about 4.62% in a certain limit case. Our
code lengths for large c are asymptotically about 5.35% of Tardos’s codes.
A part of this work was presented at 17th Applied Algebra, Algebraic Algorithms, and Error Correcting Codes (AAECC-17), Bangalore,
India, December 16–20, 2007. 相似文献