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151.
Pierre A. von Kaenel 《Fuzzy Sets and Systems》1982,8(2):199-204
A fuzzy code is defined as a fuzzy subset of n-tuples over a set F. An analysis of the Hamming distance between two fuzzy codewords and the error-correcting capability of a regular code in terms of its corresponding fuzzy code is presented. 相似文献
152.
It has been shown by Bogdanova and Boukliev [1] that there exist a ternary [38,5,24] code and a ternary [37,5,23] code. But it is unknown whether or not there exist a ternary [39,6,24] code and a ternary [38,6,23] code. The purpose of this paper is to prove that (1) there is no ternary [39,6,24] code and (2) there is no ternary [38,6,23] code using the nonexistence of ternary [39,6,24] codes. Since it is known (cf. Brouwer and Sloane [2] and Hamada and Watamori [14]) that (i) n3(6,23) = 38> or 39 and d3(38,6) = 22 or 23 and (ii) n3(6,24) = 39 or 40 and d3(39,6) = 23 or 24, this implies that n3(6,23) = 39, d3(38,6) = 22, n3(6,24) = 40 and d3(39,6) = 23, where n3<>(k,d) and d<>3(n,k) denote the smallest value of n and the largest value of d, respectively, for which there exists an [n,k,d] code over the Galois field GF(3). 相似文献
153.
The rank of a q-ary code C is the dimension of the subspace spanned by C. The kernel of a q-ary code C of length n can be defined as the set of all translations leaving C invariant. Some relations between the rank and the dimension of the kernel of q-ary 1-perfect codes, over
as well as over the prime field
, are established. Q-ary 1-perfect codes of length n=(qm − 1)/(q − 1) with different kernel dimensions using switching constructions are constructed and some upper and lower bounds for the dimension of the kernel, once the rank is given, are established.Communicated by: I.F. Blake 相似文献
154.
XOR-based Visual Cryptography Schemes 总被引:2,自引:0,他引:2
P.?TuylsEmail author H.?D.?L.?Hollmann J.?H.?Van?Lint L.?Tolhuizen 《Designs, Codes and Cryptography》2005,37(1):169-186
A recent publication introduced a Visual Crypto (VC) system, based on the polarisation of light. This VC system has goodresolution, contrast and colour properties.Mathematically, the VC system is described by the XOR operation (modulo two addition). In this paper we investigate Threshold Visual Secret Sharing schemes associated to XOR-based VC systems. Firstly, we show that n out of n schemes with optimal resolution and contrast exist, and that (2,n) schemes are equivalent to binary codes. It turns out that these schemes have much better resolution than their OR-based counterparts. Secondly, we provide two explicit constructions for general k out of n schemes. Finally, we derive bounds on the contrast and resolution of XOR-based schemes. It follows from these bounds that for k<n, the contrast is strictly smaller than one. Moreover, the bounds imply that XOR-based k out of n schemes for even k are fundamentally different from those for odd k.AMS Classification: 94A60 相似文献
155.
In this paper we show how to strengthen public-key cryptosystems against known attacks, together with the reduction of the public-key. We use properties of subcodes to mask the structure of the codes used by the conceiver of the system. We propose new parameters for the cryptosystems and even a modified Niederreiter cryptosystem in the case of Gabidulin codes, with a public-key size of less than 4000 bits.Communicated by: P. WildAMS Classification: 11T71 相似文献
156.
LU ZhiXin YU Li LI Kang LIU BingCan LIN JianGui JIAO RongZhen & YANG BoJun School of Science Beijing University of Posts Telecommunications Beijing China Key Laboratory of Information Photonics Optical Communication Ministry of Education 《中国科学:物理学 力学 天文学(英文版)》2010,(1)
An efficient and practical post-processing technique based on reverse reconciliation for continuous variable quantum key distribution is proposed and simulated with low-density parity check (LDPC) codes. MultiLevel Coding/ MultiStage Decoding, which fully utilizes optimization technique such as vector quantization and iterative decoding and the optimal channel coding most close to the Shannon limit, was used to realize efficient reverse reconciliation algorithm. Simulation results showed that the proposed m... 相似文献
157.
For q = p
m
and m ≥ 1, we construct systematic authentication codes over finite field using Galois rings. We give corrections of the construction of [2]. We generalize corresponding systematic authentication codes of [6] in various ways. 相似文献
158.
We determine the structure of cyclic codes over
for arbitrary even length giving the generator polynomial for these codes. We determine the number of cyclic codes for a
given length. We describe the duals of the cyclic codes, describe the form of cyclic codes that are self-dual and give the
number of these codes. We end by examining specific cases of cyclic codes, giving all cyclic self-dual codes of length less
than or equal to 14.
San Ling - The research of the second named author is partially supported by research Grants MOE-ARF R-146-000-029-112 and
DSTA R-394-000-011-422. 相似文献
159.
《Discrete Mathematics》2018,341(10):2708-2719
160.
We investigate the relationship between two constructions of maximal comma-free codes described, respectively, by Eastman and by Scholtz and the notions of Hall sets and Lazard sets introduced in connection with factorizations of free monoids and bases of free Lie algebras. 相似文献