共查询到20条相似文献,搜索用时 15 毫秒
1.
A note on generalized Hamming weights of BCH(2) 总被引:1,自引:0,他引:1
van der Vlugt M. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1996,42(1):254-256
Determines results for the first six generalized Hamming weights of double-error-correcting primitive binary BCH codes 相似文献
2.
Generalized Hamming weights of linear codes 总被引:4,自引:0,他引:4
Helleseth T. Klove T. Ytrehus O. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1992,38(3):1133-1140
The generalized Hamming weight, d r(C ), of a binary linear code C is the size of the smallest support of any r -dimensional subcode of C . The parameter d r(C ) determines the code's performance on the wire-tap channel of Type II. Bounds on d r(C ), and in some cases exact expressions, are derived. In particular, a generalized Griesmer bound for d r(C ) is presented and examples are given of codes meeting this bound with equality 相似文献
3.
Generalized Hamming weights for linear codes 总被引:15,自引:0,他引:15
Wei V.K. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1991,37(5):1412-1418
Motivated by cryptographical applications, the algebraic structure, of linear codes from a new perspective is studied. By viewing the minimum Hamming weight as a certain minimum property of one-dimensional subcodes, a generalized notion of higher-dimensional Hamming weights is obtained. These weights characterize the code performance on the wire-tap channel of type II. Basic properties of generalized weights are derived, the values of these weights for well-known classes of codes are determined, and lower bounds on code parameters are obtained. Several open problems are also listed 相似文献
4.
Generalized Hamming weights of q-ary Reed-Muller codes 总被引:3,自引:0,他引:3
Heijnen P. Pellikaan R. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1998,44(1):181-196
The order bound on generalized Hamming weights is introduced in a general setting of codes on varieties which comprises both the one point geometric Goppa codes as well as the q-ary Reed-Muller codes. For the latter codes it is shown that this bound is sharp and that they satisfy the double chain condition 相似文献
5.
Helleseth T. Hove B. Kyeongcheol Yang 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1999,45(4):1255-1258
This article contains results on the generalized Hamming weights (GHW) for the Goethals and Preparata codes over Z4. We give an upper bound on the rth generalized Hamming weights dr(m,j) for the Goethals code Gm(j) of length 2m over Z 4, when m is odd. We also determine d3.5(m,j) exactly. The upper bound is shown to be tight up to r=3.5. Furthermore, we determine the rth generalized Hamming weight dr(m) for the Preparata code of length 2m over Z4 when r=3.5 and r=4 相似文献
6.
Generalized Hamming weights of BCH(3) revisited 总被引:1,自引:0,他引:1
Van der Geer G. Van der Vlugt M. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1995,41(1):300-301
Determines the first five generalized Hamming weights of 3-error-correcting primitive binary BCH-codes 相似文献
7.
Changshik Shim Habong Chung 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1995,41(3):805-808
The generalized Hamming weight of a linear code is a new notion of higher dimensional Hamming weights. Let C be an [n,k] linear code and D be a subcode. The support of D is the cardinality of the set of not-always-zero bit positions of D. The rth generalized Hamming weight of C, denoted by dr(C), is defined as the minimum support of an r-dimensional subcode of C. It was shown by Wei (1991) that the generalized Hamming weight hierarchy of a linear code completely characterizes the performance of the code on the type II wire-tap channel defined by Ozarow and Wyner (1984). In the present paper the second generalized Hamming weight of the dual code of a double-error-correcting BCH code is derived and the authors prove that except for m=4, the second generalized Hamming weight of [2m-1, 2m]-dual BCH codes achieves the Griesmer bound 相似文献
8.
Ashikhmin A. Barg A. Litsyn S. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1999,45(4):1258-1263
We derive new asymptotic upper bounds on the generalized weights of a binary linear code of a given size. We also prove some asymptotic results on the distance distribution of binary codes 相似文献
9.
10.
On the Hamming distance properties of group codes 总被引:1,自引:0,他引:1
Forney G.D. Jr. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1992,38(6):1797-1801
Under certain mild conditions, the minimum Hamming distance D of an (N , K , D ) group code C over a non-abelian group G is bounded by D ⩽N -2K +2 if K ⩽N /2, and is equal to 1 if K >N /2. Consequently, there exists no (N , K , N -K +1) group code C over an non-abelian group G if 1<K <N . Moreover, any normal code C with a non-abelian output space has minimum Hamming distance equal to D =1. These results follow from the fact that non-abelian groups have nontrivial commutator subgroups. Finally, if C is an (N , K , D ) group code over an abelian group G that is not elementary abelian, then there exists an (N , K , D ) group code over a smaller elementary abelian group G '. Thus, a group code over a general group G cannot have better parameters than a conventional linear code over a field of the same size as G 相似文献
11.
Shortened Hamming codes are widely used for error detection in data communications. In this paper, a method for computing the probability of an undetected error for these codes is presented. This method is then used to evaluate the error-detection performance of the shortened codes obtained from the two distance-4 Hamming codes adopted by CCITT X.25 for error control for packet-switched networks. We show that shortening a code does affect its error-detection performance. 相似文献
12.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1977,23(5):592-597
Discrete-time source coding theorems are established for more general reproduction alphabets than allowed in previous results on coding for a class of sources subject to a fidelity constraint. The two different alphabets considered are metric spaces for which every closed bounded subset is compact and separable Hilbert spaces. Potential applications of the Hilbert space results to continuous-time source coding are discussed. 相似文献
13.
M. I. Mazurkov 《Radioelectronics and Communications Systems》2009,52(12):643-648
A recurrent algorithm has been developed for building complete classes of the generalized space-time block codes of arbitrary
size G(2
k
×2
k
), k=2, 3, …, ∞ over the complex and real alphabets. The orthogonal space-time codes offered are referred to the high-speed class,
because they possess a fixed transmission rate R = 3/4 > 1/2; in this case, the number of transmitting antennas can be easily controlled on the basis of condition N
T
≤ 2
k
. 相似文献
14.
15.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1983,29(3):345-348
Ifm is odd andsigma /in Aut GF(2^{m}) is such thatx rightarrow x^{sigma^{2}-1} is1-1 , there is a[2^{m+1}-1,2^{m+l}-2m-2] nonlinear binary codeP(sigma) having minimum distance 5. All the codesP(sigma) have the same distance and weight enumerators as the usual Preparata codes (which rise asP(sigma) whenx^{sigma}=x^{2}) . It is shown thatP(sigma) andP(tau) are equivalent if and only iftau=sigma^{pm 1} , andAut P(sigma) is determined. 相似文献
16.
The Hamming network is a binary associative memory which exhibits the maximum theoretically obtainable performance in terms of capacity and associativity. The structure is not ideal and two modifications which reduce the number of connections in the correlation matrix and in the selection layers are suggested. These modifications offer a significant reduction in the number of calculations required.<> 相似文献
17.
Ericson T. Levenshtein V.I. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1994,40(6):1882-1893
We consider the problem of simultaneous identification and transmission of information by means of superimposed codes. It is assumed that a total population of T users share a common channel. At each time at most in of the T users are active. The output from the channel is the modulo-2 sum of the binary codewords transmitted by the active users, possibly disturbed by errors. A superimposed code is actually a set of codes-one for each user-designed in such a way that both the (at most) m active users and their messages can be identified, even in the presence of a permissible number of errors in the channel. We give several explicit constructions for superimposed codes and analyze in detail their performance. In several of the cases under study we offer codes that are proved to be best possible 相似文献
18.
We present hardware performance analyses of Hamming product codes combined with type-II hybrid automatic repeat request (HARQ), for on-chip interconnects. Input flit width and the number of rows in the product code message are investigated for their impact on the number of wires in the link, codec delay, reliability, and energy consumption. Analytical models are presented to estimate codec delay and residual flit error rate. The analyses are validated by comparison with simulation results. In a case study using H.264 video encoder in a network-on-chip environment, the method of combining Hamming product codes with type-II HARQ achieves several orders of magnitude improvement in residual flit error rate. For a given residual flit error rate requirement (e.g., 10-20), this method yields up to 50% energy improvement over other error control methods in high-noise conditions. 相似文献
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20.
Kapur A. Varanasi M.K. Mullis C.T. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2005,51(6):2220-2224
This correspondence characterizes the performance limitation of the well-acclaimed generalized Welch-bound equality (WBE) signals under linear minimum mean-squared error (MMSE) detection. It is analytically proven, and experimentally verified, that when users in an overloaded but finite-size code-division multiple-access (CDMA) system are allocated such signals, the error rate of at least one user "floors" (i.e., it cannot be driven to zero even in the absence of additive noise), independently of the symbol energies. If, in addition, all users are received with equal energy, then the error rate of every user "floors". 相似文献