共查询到20条相似文献,搜索用时 15 毫秒
1.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1972,18(6):824-825
For1 leq i leq m - s- 2 and0 leq s leq m -2i , the intersection of the binary BCH code of designed distance2 ^{m-s-1} - 2 ^{m-s-t-1} - 1 and length2^m - 1 with the shortened(s + 2) th-order Reed-Muller code of length2^m -- 1 has codewords of weight2^{m-s-1} - 2^{m-s-t-1} - 1 . 相似文献
2.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1986,32(5):706-709
Recently Kasami {em et al.} presented a linear programming approach to the weight distribution of binary linear codes [2]. Their approach to compute upper and lower bounds on the weight distribution of binary primitive BCH codes of length2^{m} - 1 withm geq 8 and designed distance2t + 1 with4 leq t leq 5 is improved. From these results, the relative deviation of the number of codewords of weightjleq 2^{m-1} from the binomial distribution2^{-mt} left( stackrel{2^{m}-1}{j} right) is shown to be less than 1 percent for the following cases: (1)t = 4, j geq 2t + 1 andm geq 16 ; (2)t = 4, j geq 2t + 3 and10 leq m leq 15 ; (3)t=4, j geq 2t+5 and8 leq m leq 9 ; (4)t=5,j geq 2t+ 1 andm geq 20 ; (5)t=5, j geq 2t+ 3 and12 leq m leq 19 ; (6)t=5, j geq 2t+ 5 and10 leq m leq 11 ; (7)t=5, j geq 2t + 7 andm=9 ; (8)t= 5, j geq 2t+ 9 andm = 8 . 相似文献
3.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1976,22(3):348-349
The coset leader of greatest weight in the 3-error-correcting BCH code of length2^{m}-1 has weight 5, for oddm geq 5 . 相似文献
4.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1976,22(2):138-147
An extensive study of binary triple-error-correcting codes of primitive lengthn = 2^{m} - 1 is reported that results in a complete decoding algorithm whenever the maximum coset weightW_{max} is five. In this regard it is shown thatW_{max} = 5 when four dividesm , and strong support is provided for the validity of the conjecture thatW_{max} = 5 for allm . The coset weight distribution is determined exactly in some cases and bounded in others. 相似文献
5.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1978,24(2):257-258
Van der Horst and Berger have conjectured that the covering radius of the binary 3-error-correcting Bose-Chaudhuri-Hocquenghem (BCH) code of length2^{m} - l, m geq 4 is 5. Their conjecture was proved earlier whenm equiv 0, 1 , or 3 (mod 4). Their conjecture is proved whenm equiv 2 (mod 4). 相似文献
6.
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
7.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1983,29(3):448-450
We present an efficient maximum likelihood decoding algorithm for the punctured binary Reed-Muller code of order(m - 3) and length2^{m} - 1, M geq 3 , and we give formulas for the weight distribution of coset leaders of such codes. 相似文献
8.
《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
9.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1976,22(6):737-745
A particular shortening technique is applied to majority logic decodable codes of length2^{t} . The shortening technique yields new efficient codes of lengthsn = 2^{p} , wherep is a prime, e.g., a (128,70) code withd_{maj} = 16 . For moderately long code lengths (e.g.,n = 2^{11} or 2^{13}) , a 20-25 percent increase in efficiency can be achieved over the best previously known majority logic decodable codes. The new technique also yields some efficient codes for lengthsn = 2^{m} wherem is a composite number, for example, a (512,316) code withd_{maj} = 32 code which has 42 more information bits than the previously most efficient majority logic decodable code. 相似文献
10.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1981,27(5):548-555
An infinite sequence ofk -dimensional binary linear block codes is constructed with parametersn=2^{k}+2^{k-2}-15,d=2^{k-1}+2^{k-3}-8,k geq 7 . Fork geq 8 these codes are unique, while there are five nonisomorphic codes fork=7 . By shortening these codes in an appropriate way, one finds codes meeting the Griesmer bound for2^{k-1}+2^{k-3}-15 leq d leq 2^{k-1}+2^{k-3}-8; k geq 7 . 相似文献
11.
Construction of de Bruijn sequences of minimal complexity 总被引:1,自引:0,他引:1
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1984,30(5):705-709
It is well known that the linear complexity of a de Bruijn sequenceS of length2^{n} is bounded below by2^{n- 1} + n forn geq 3 . It is shown that this lower bound is attainable for alln . 相似文献
12.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1979,25(1):110-112
A recent paper [1] discussed the2^{-p} bound (wherep = n- k ) for the probability of undetected errorP(epsilon) for an(n,k) block code used for error detection on a binary symmetric channel. This investigation is continued and extended and dual codes are studied. The dual and extension of a perfect code obey the2^{-p} bound, but this is not necessarily true for arbitrary codes that obey the bound. Double-error-correcting BCH codes are shown to obey the bound. Finally the problem of constructing uniformly good codes is examined. 相似文献
13.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1978,24(5):627-628
Upper bounds on the covering radius of binary codes are studied. In particular it is shown that the covering radiusr_{m} of the first-order Reed-Muller code of lenglh2^{m} satisfies2^{m-l}-2^{lceil m/2 rceil -1} r_{m} leq 2^{m-1}-2^{m/2-1} . 相似文献
14.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1970,16(6):745-751
In this paper, we establish the following result. Theorem:A_i , the number of codewords of weighti in the second-order binary Reed-Muller code of length2^m is given byA_i = 0 unlessi = 2^{m-1} or2^{m-1} pm 2^{m-l-j} , for somej, 0 leq j leq [m/2], A_0 = A_{2^m} = 1 , and begin{equation} begin{split} A_{2^{m-1} pm 2^{m-1-j}} = 2^{j(j+1)} &{frac{(2^m - 1) (2^{m-1} - 1 )}{4-1} } \ .&{frac{(2^{m-2} - 1)(2^{m-3} -1)}{4^2 - 1} } cdots \ .&{frac{(2^{m-2j+2} -1)(2^{m-2j+1} -1)}{4^j -1} } , \ & 1 leq j leq [m/2] \ end{split} end{equation} begin{equation} A_{2^{m-1}} = 2 { 2^{m(m+1)/2} - sum_{j=0}^{[m/2]} A_{2^{m-1} - 2^{m-1-j}} }. end{equation} 相似文献
15.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1977,23(6):776-778
It is shown that a high-radix fast Fourier transform (FFT) with generatorgamma = 3 over GF(F_{n}) , whereF_{n} = 2^{2}^{n'} + 1 is a Fermat prime, can be used for encoding and decoding of Reed-Solomon (RS) codes of length2^{2}^{n} . Such an RS decoder is considerably faster than a decoder using the usual radix 2 FFT. This technique applies most ideally to a 16-error-correcting, 256-symbol RS code of 8 bits being considered currently for space communication applications. This special code can be encoded and decoded rapidly using a high-radix FFT algorithm over GF(F_{3}) . 相似文献
16.
Some long cyclic linear binary codes are not so bad 总被引:1,自引:0,他引:1
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1974,20(3):351-356
We show that when an inner linear cyclic binary code which has an irreducible check polynomial is concatenated with an appropriately chosen maximal-distance-separable outer code, then the overall code is cyclic OverGF(2) . Using this theorem, we construct a number of linear cyclic binary codes which are better than any previously known. In particular, by taking the inner code to be a quadratic residue code, we obtain linear cyclic binary codes of lengthN , rateR , and distanceD geq (1 - 2R)N/ sqrt{2 log N} , which compares favorably with the BCH distanceD sim (2 ln R^{-1})N/log N , although it still fails to achieve the linear growth of distance with block length which is possible with noncyclic linear concatenated codes. While this construction yields many codes, including several with block lengths greater than10^{10^5} , we have not been able to prove that there are arbitrarily long codes of this type without invoking the Riemann hypothesis or the revised Artin conjecture, as the existence of long codes of our type is equivalent to the existence of large primesp for which the index of 2 is(p - 1)/2 . 相似文献
17.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1979,25(3):361-362
Gorenstein, Peterson, and Zierler have conjectured that not -error-correcting BCH code of length2^{m} - 1 witht > 2 is quasi-perfect. This conjecture is proved. The covering radius of a code is defined as the smallest integerrho such that the union of the spheres of radius ia about the codewords equals the containing space. 相似文献
18.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1972,18(1):192-196
We show what choice there is in assigning output digits to transitions of a binary rate1/n code trellis so that the latter will correspond to a convolutional code. We then prove that in any ratefrac{1}{2} noncatastrophic code of constraint lengthupsilon each binary sequence of length2j (1 leq j leq upsilon - 1) is associated with exactly2^{upsilon -j -1} distinct pathsj branches long. As a consequence of the above properties nondegenerate codes with branch complementarity are fully determined by the topological relationship of the trellis transitions associated with output pairs 00. Finally, we derive a new upper bound on free distance of rate1/n convolutional codes and use our results to determine the length of the largest input sequence that can conceivably result in an output whose weight is 相似文献
19.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1984,30(2):395-403
For any(n, k, d) binary linear code, the Griesmer bound says thatn geq sum_{i=0}^{k-1} lceil d/2^{i} rceil , wherelceil x rceil denotes the smallest integergeq x . We consider codes meeting the Griesmer bound with equality. These codes have parametersleft( s(2^{k} - 1) - sum_{i=1}^{p} (2^{u_{i}} - 1), k, s2^{k-1} - sum_{i=1}^{p} 2^{u_{i} -1} right) , wherek > u_{1} > cdots > u_{p} geq 1 . We characterize all such codes whenp = 2 oru_{i-1}-u_{i} geq 2 for2 leq i leq p . 相似文献
20.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1976,22(2):235-237
In the past, it has generally been assumed that the probability of undetected error for an(n,k) block code, used solely for error detection on a binary symmetric channel, is upperbounded by2^{-(n-k)} . In this correspondence, it is shown that Hamming codes do indeed obey this bound, but that the bound is violated by some more general codes. Examples of linear, cyclic, and Bose-Chaudhuri-Hocquenghem (BCH) codes which do not obey the bound are given. 相似文献