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1.
Trieu-Kien Truong Chong-Dao Lee Yaotsu Chang Wen-Ku Su 《Communications, IEEE Transactions on》2009,57(5):1221-1224
This letter proposes a novel scheme which consists of a weight-counting algorithm, the combinatorial designs of the Assmus-Mattson theorem, and the weight polynomial of Gleason?s theorem to determine the weight distributions of binary extended quadratic residue codes. As a consequence, the weight distributions of binary (138, 69, 22) and (168, 84, 24) extended quadratic residue codes are given. 相似文献
2.
Chong-Dao Lee Yan-Haw Chen Yaotsu Chang 《Communications Letters, IEEE》2009,13(2):139-141
This letter proposes an improved and unified method to determine the weight enumerators of binary extended quadratic residue (EQR) codes. It is faster than the previous methods for some of binary EQR codes. Moreover, all the results for the weight enumerators of binary EQR codes are listed. 相似文献
3.
Cyclotomy and duadic codes of prime lengths 总被引:2,自引:0,他引:2
Cunsheng Ding Pless V. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1999,45(2):453-466
We present a cyclotomic approach to the construction of all binary duadic codes of prime lengths. We calculate the number of all binary duadic codes for a given prime length and that of all duadic codes that are not quadratic residue codes. We give necessary and sufficient conditions for p such that all binary duadic codes of length p are quadratic residue (QR) codes. We also show how to determine some weights of duadic codes with the help of cyclotomic numbers 相似文献
4.
The weight distributions of the (13, 6) and the (17, 8) quaternary quadratic residue codes are computed. 相似文献
5.
The extended quadratic residue code is the only (48,24,12) self-dual doubly-even code 总被引:3,自引:0,他引:3
Houghten S.K. Lam C.W.H. Thiel L.H. Parker J.A. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2003,49(1):53-59
An extremal self-dual doubly-even binary (n,k,d) code has a minimum weight d=4/spl lfloor/n/24/spl rfloor/+4. Of such codes with length divisible by 24, the Golay code is the only (24,12,8) code, the extended quadratic residue code is the only known (48,24,12) code, and there is no known (72,36,16) code. One may partition the search for a (48,24,12) self-dual doubly-even code into three cases. A previous search assuming one of the cases found only the extended quadratic residue code. We examine the remaining two cases. Separate searches assuming each of the remaining cases found no codes and thus the extended quadratic residue code is the only doubly-even self-dual (48,24,12) code. 相似文献
6.
Xuemin Chen Reed I.S. Truong T.K. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1994,40(2):503-504
The class of binary quadratic residue (QR) codes of length n=8m-1 contains two perfect codes. These are the (7,4,3) Hamming code and the (23,12,7) Golay code. However, it is proved in the present paper that there are no quasi-perfect QR codes of length 8m-1. Finally, this result is generalized to all binary self-dual codes of length N>72 相似文献
7.
Xuemin Chen Reed I.S. Truong T.K. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1994,40(1):126-136
The 1/2-rate binary quadratic residue (QR) codes, using binary phase-shift keyed (BPSK) modulation and hard decoding, are presented as an efficient system for reliable communication. Performance results of error correction are obtained both theoretically and by means of computer calculations for a number of binary QR codes. These results are compared with the commonly used 1/2-rate convolutional codes with constraint lengths from 3 to 7 for the hard-decision case. The binary QR codes of different lengths are shown to be equivalent in error-correction performance to some 1/2-rate convolutional codes, each of which has a constraint length K that corresponds to the error-control rate d/n and the minimum distance d of the QR codes 相似文献
8.
Lazic D.E. Kalouti H. Beth T. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1998,44(1):294-295
Usually spectra (weight distributions) of primitive binary BCH codes are supposed to approximate binomial weight distributions well for a wide range of code rates and code lengths. It is shown that for any fixed code rate R<1 spectra of long (N→∞) primitive binary BCH codes cannot approximate the binomial distribution at all 相似文献
9.
本文利用Johnson Schemes理论研究了二元等重码及其最大码字数问题.在Delsarte的associate schemes理论中,Q-变换被引入以研究二元等重码的距离分布.首先,本文研究了等重码距离分布的Q-变换;然后,通过使用Q-变换的性质,我们研究了二元等重码的最大码字数问题并得到码字数的一个新的上界,该上界在形式上类似于纠错码理论中的Grey-Rankin界,并且在某些情况下优于已知的结果. 相似文献
10.
Duadic Codes 总被引:3,自引:0,他引:3
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1984,30(5):709-714
A new family of binary cyclic(n,(n + 1)/2) and(n,(n - 1)/2) codes are introduced, which include quadratic residue (QR) codes whenn is prime. These codes are defined in terms of their idempotent generators, and they exist for all oddn = p_{1}^{a_{1}} p_{2}^{a_{2}} cdots p_{r}^{a_{r}} where eachp_{i} is a primeequiv pm 1 pmod{8} . Dual codes are identified. The minimum odd weight of a duadic(n,(n + 1)/2) code satisfies a square root bound. When equality holds in the sharper form of this bound, vectors of minimum weight hold a projective plane. The unique projective plane of order 8 is held by the minimum weight vectors in two inequivalent(73,37,9) duadic codes. All duadic codes of length less than127 are identified, and the minimum weights of their extensions are given. One of the duadic codes of length113 has greater minimum weight than the QR code of that length. 相似文献
11.
Charpin P. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1994,40(5):1425-1442
Let B be the binary two-error-correcting BCH code of length 2m-1 and let Bˆ be the extended code of B. We give formal expressions of weight distributions of the cosets of the codes Bˆ only depending on m. We can then deduce the weight distributions of the cosets of B. When m is odd, it is well known that there are four distinct weight distributions for the cosets of B. So our main result is about the even case. Camion, Courteau, and Montpetit (see ibid., vol.38, no.7, p.1353, 1992) observe that for the lengths 15, 63, and 255 there are eight distinct weight distributions. We prove that this property holds for the codes Bˆ and B for all even m 相似文献
12.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1967,13(2):335-336
In this correspondence, we consider nonlinear binary error-correcting codes based upon then -fold interleaving of a periodic binary sequence of lengthL with out-of-phase (normalized) autocorrelation-1/L . Examples of binary sequences with such out-of-phase autocorrelation (termed two-level sequences) are: 1) maximal-length linear shift-register footnote[1]{sequences}, 2) twin-prime footnote[2]{sequences}, 3) quadratic residue footnote[3]{sequences}, and 4) Hall foonote[4]{sequences}. 相似文献
13.
MacMullan S.J. Collins O.M. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1998,44(1):197-214
This paper analyzes the performance of concatenated coding systems operating over the binary-symmetric channel (BSC) by examining the loss of capacity resulting from each of the processing steps. The techniques described in this paper allow the separate evaluation of codes and decoders and thus the identification of where loss of capacity occurs. They are, moreover, very useful for the overall design of a communications system, e.g., for evaluating the benefits of inner decoders that produce side information. The first two sections of this paper provide a general technique (based on the coset weight distribution of a binary linear code) for calculating the composite capacity of the code and a BSC in isolation. The later sections examine the composite capacities of binary linear codes, the BSC, and various decoders. The composite capacities of the (8,4) extended Hamming, (24, 12) extended Golay, and (48, 24) quadratic residue codes appear as examples throughout the paper. The calculations in these examples show that, in a concatenated coding system, having an inner decoder provide more information than the maximum-likelihood (ML) estimate to an outer decoder is not a computationally efficient technique, unless generalized minimum-distance decoding of an outer code is extremely easy. Specifically, for the (8,4) extended Hamming and (24, 12) extended Golay inner codes, the gains from using any inner decoder providing side information, instead of a strictly ML inner decoder, are shown to be no greater than 0.77 and 0.34 dB, respectively, for a BSC crossover probability of 0.1 or less, However, if computationally efficient generalized minimum distance decoders for powerful outer codes, e.g., Reed-Solomon codes, become available, they will allow the use of simple inner codes, since both simple and complex inner codes have very similar capacity losses 相似文献
14.
We have generated binary images of a large number of shortened cyclic (8, 5) codes over GF(2/sup 8/) and have computed weight distributions of the binary images of the codes. Based on the weight distributions, we have chosen four codes with the largest minimum weight 8 and the second largest minimum weight 7 among the generated codes. Over an additive white Gaussian noise channel with binary phase-shift keying modulation, simulation results have shown that block error rates of the chosen codes by a soft-decision decoding based on order-2 reprocessing are smaller than those of (64, 40) subcodes of Reed-Muller (64, 42) code by maximum likelihood decoding. 相似文献
15.
Ozeki M. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2000,46(7):2359-2372
We present a method to determine the complete coset weight distributions of doubly even binary self-dual extremal [56, 28, 12] codes. The most important steps are (1) to describe the shape of the basis for the linear space of rigid Jacobi polynomials associated with such codes in each index i, (2) to describe the basis polynomials for the coset weight enumerators of the assigned coset weight i by means of rigid Jacobi polynomials of index i. The multiplicity of the cosets of weight i have a connection with the frequency of the rigid reference binary vectors v of weight i for the Jacobi polynomials. This information is sufficient to determine the complete coset weight distributions. Determination of the covering radius of the codes is an immediate consequence of this method. One important practical advantage of this method is that it is enough to get information on 8190 codewords of weight 12 (minimal-weight words) in each such code for computing every necessary information 相似文献
16.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1985,31(6):769-780
Binary primitive BCH codes form a large class of powerful error-correcting codes. The weight distributions of primitive BCH codes are unknown except for some special classes, such as the single, double, triple error-correcting codes and some very low-rate primitive BCH codes. However, asymptotic results for the weight distribution of a large subclass of primitive BCH codes have been derived by Sidel'nikov. These results provide some insight into the weight structure of primitive BCH codes. Sidel'nikov's approach is improved and applied to the weight distribution of any binary linear block code. Then Sidel'nikov's results on the weight distributions of binary primitive BCH codes are improved and it is shown that the weights of a binary primitive code have approximate binomial distribution. 相似文献
17.
Weight enumerators of self-dual codes 总被引:4,自引:0,他引:4
Brualdi R.A. Pless V.S. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1991,37(4):1222-1225
Some construction techniques for self-dual codes are investigated, and the authors construct a singly-even self-dual [48,24,10]-code with a weight enumerator that was not known to be attainable. It is shown that there exists a singly-even self-dual code C ' of length n =48 and minimum weight d =10 whose weight enumerator is prescribed in the work of J.H. Conway et al. (see ibid., vol.36, no.5, p.1319-33, 1990). Two self-dual codes of length n are called neighbors, provided their intersection is a code of dimension (n /2)-1. The code C' is a neighbor of the extended quadratic residue code of length 48 相似文献
18.
A novel decoding scheme, called syndrome-weight determination, was proposed by Chang et al. in 2008 for the Golay code, or the (23, 12, 7) quadratic residue code. This method is not only very simple in principle but also suitable for parallel hardware design. Presented is a modified version for any binary quadratic residue codes which has been developed. Because of its regular property, the proposed decoder is suitable for both software design and hardware development. 相似文献
19.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1980,26(2):223-227
Forp eqiv pm 1 pmod{8} there are two binary codes,Q(p) andN(p) , each an extended quadratic residue code of lengthp+1 and dimension(p+1)/2 . The existence of double circulant generator matrices for these codes is investigated. A possibly infinite family of primesp is presented for whichQ(p) andN(p) must have double circulant generator matrices. Two counterexamples prove the construction is not always possible. 相似文献
20.
A systematic construction of self-dual codes 总被引:1,自引:0,他引:1
Carlach J.-C. Otmani A. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2003,49(11):3005-3009
A new coding construction scheme of block codes using short base codes and permutations that enables the construction of binary self-dual codes is presented in Cadic et al. (2001) and Carlach et al. (1999, 2000). The scheme leads to doubly-even (resp,. singly-even) self-dual codes provided the base code is a doubly-even self-dual code and the number of permutations is even (resp., odd). We study the particular case where the base code is the [8, 4, 4] extended Hamming. In this special case, we construct a new [88, 44, 16] extremal doubly-even self-dual code and we give a new unified construction of the five [32, 16, 8] extremal doubly-even self-dual codes. 相似文献