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Page 9004 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
Summary: “In this correspondence, we give a new definition of generalized Hamming weights of nonlinear codes and a new in- terpretation connected with it.  ...  Since perfect codes of length n = 3 and 7 are unique, the existence of nonsystematic perfect binary codes is fully established.  ... 

Coding of fingerprint images using binary subband decomposition and vector quantization

Oemer N. Gerek, Enis A. Cetin, Sarah A. Rajala, Majid Rabbani
1998 Visual Communications and Image Processing '98  
In our method, the fingerprint image is first processed by a binary nonlinear subband decomposition filter bank and the resulting subimages are coded using vector quantizers designed for quantizing binary  ...  In this paper, compression of binary digital fingerprint images is considered. High compression ratios for fingerprint images is essential for handling huge amount of images in databases.  ...  Either the centroids are kept gray valued and the iteration is repeated by setting the new vector boundaries according to the new centroids, or the centroids are quantized to binary and the new boundaries  ... 
doi:10.1117/12.298317 fatcat:fk4atq7fffauhde4xbysfnn5ky

Page 5741 of Mathematical Reviews Vol. , Issue 85m [page]

1985 Mathematical Reviews  
Examples of t-perfect codes are the codes consisting of only one codeword of length at most t, and the binary repetition codes of length 2¢ +1.  ...  Other examples of perfect codes are the 1- perfect Hamming binary and, more generally, g-ary codes and the 3-perfect binary Golay code of length 23. A. Tietavainen and A. Perko [Ann. Univ. Turku.  ... 

Page 752 of Mathematical Reviews Vol. , Issue 2002A [page]

2002 Mathematical Reviews  
[Lobstein, Antoine-Christophe] On generalized concatenated constructions of perfect binary nonlinear codes. (Russian.  ...  A variation of the generalized concatenated code construction is used for the construction of a large number of nonlinear binary perfect codes of minimum distance 3.  ... 

Page 3063 of Mathematical Reviews Vol. , Issue 83h [page]

1983 Mathematical Reviews  
A new method for generating a nonlinear binary cyclic shift sequence of length T (1<7<2") which can be generated by the proposed system is discussed using a binary graph G” corresponding to the state transition  ...  We present a new class of linear codes, which simplifies the decoding process by adopting a concept of product code and improves the efficiency by mod-2 superimposing a new code on the basic codes.  ... 

A polynomial construction of perfect codes

G.D. Nguyen
1997 Computers and Mathematics with Applications  
Starting with a single-error-correcting extended perfect binary systematic code of length S, one can construct a single-error-correcting extended perfect binary systematic code of length 82 s by polynomial  ...  Given two extended perfect binary codes of lengths $I and $2, one can construct an extended perfect binary code of length SRS2 by the Phelps scheme [5] .  ...  If nonlinear perfect codes exist, they must have the same parameters as Hamming codes [1, pp. 179-187]. Vasilev [2] constructed a family of nonlinear perfect codes in 1962.  ... 
doi:10.1016/s0898-1221(97)00060-6 fatcat:dwuz3gojx5bb3agrkjzhi4yobi

Page 2237 of Mathematical Reviews Vol. , Issue 85e [page]

1985 Mathematical Reviews  
An algebraic theory of systematic nonlinear binary codes is de- veloped; the main tool is the Jacobian matrix of a code.  ...  The results are applied to construct new, perfect, single error correcting codes. N. J. Patterson (Princeton, N.J.) 85e:94023 Phelps, K. T. (1-GAIT) A combinatorial construction of perfect codes.  ... 

Efficient representation of binary nonlinear codes: constructions and minimum distance computation

Mercè Villanueva, Fanxuan Zeng, Jaume Pujol
2014 Designs, Codes and Cryptography  
Algorithms to compute the minimum distance of binary nonlinear codes, based on known algorithms for linear codes, are also established, along with an algorithm to decode such codes.  ...  Moreover, some properties and constructions of new codes from given ones in terms of this representation are described.  ...  It is known that there are exactly 5983 binary perfect codes of length 15 and 2165 binary extended perfect codes of length 16, each one having 2048 codewords [19] .  ... 
doi:10.1007/s10623-014-0028-4 fatcat:3gouxcncfrhzna6eyh4qnbvd74

Page 1968 of Mathematical Reviews Vol. 56, Issue 5 [page]

1978 Mathematical Reviews  
They obtain bounds on achievable rates for uniquely decodable code pairs, provide a list of such codes found by @ computer search, and introduce a new class of 4-decodable code | 15140 | { 15141 | pairs  ...  Information Theory IT-22 (1976), no. 2, 129-137; | MR 53 #5152] on coding for the two-access binary erasure channel.  ... 

Page 8299 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
(RS-AOSSI: Novosibirsk) On the construction of perfect nonlinear binary codes by symbol inversion. (Russian. Russian summary ) Diskretn. Anal. Issled. Oper.  ...  . \ 4 (1997), no. 1, 46-52, 90 Summary (translated from the Russian): “We present a method for constructing perfect nonlinear binary codes with single-error correction, which consists in the inversion  ... 

Optimal Constant Composition Codes From Zero-Difference Balanced Functions

Cunsheng Ding
2008 IEEE Transactions on Information Theory  
For information on perfect nonlinear functions, the reader is referred to [5] , [6] , [15] , [21] , [22] . B.  ...  So the construction of optimal constant composition codes of Section IV-B is indeed a generalization of the one using perfect nonlinear functions presented in [15] .  ...  Based on consta-cyclic simplex codes, a new explicit construction of a family of 2-generator quasi-twisted (QT) two-weight codes is presented.  ... 
doi:10.1109/tit.2008.2006420 fatcat:om7nxbjhsvcevhrmgc7frwceym

On the size of the symmetry group of a perfect code

Olof Heden
2011 Discrete Mathematics  
It is shown that for every nonlinear perfect code C of length n and rank r with n − log(n + 1) where Sym(C ) denotes the group of symmetries of C .  ...  The code C is a perfect 1-error correcting binary code, here for short a perfect code, if to any wordx of Z n 2 there is a unique wordc of C at distance at most one fromx.  ...  Analyzing the derivation in Section 3 of our new bound, one may observe that we make use of the nonlinearity only when applying Lemma 3.  ... 
doi:10.1016/j.disc.2011.05.002 fatcat:hoc2lt7sgrfnnfso6rceyx2eem

Cumulative subject index volumes 33–35

1977 Information and Control  
, 33, 210 cyclic, binary: weights of code words, 34 , 130 nearly perfect, over finite fields: all known, 35, 40 perfect, group and nongroup: new construction, 34, 314 semiregular convolutional  ...  nonlinear, dense orbital behavior, 35, 246 Disjunctive languages on free monoid, 34, 123 Distributed parameter nonlinear, systems: observability and controllability for, 34, 348 Edge detection  ... 
doi:10.1016/s0019-9958(77)90187-5 fatcat:jaxd23nbmva5hdnq37lof736um

Page 2557 of Mathematical Reviews Vol. 57, Issue 6 [page]

1979 Mathematical Reviews  
on Goppa codes and their applications to con- structing efficient binary codes.  ...  N. 57 #19078 A remark on two classes of nonlinear codes. (Russian) Problemy Peredaéi Informacii 10 (1974), no. 2, 61-63.  ... 

Perfect binary codes: bounds and properties

F.I. Solov'eva
2000 Discrete Mathematics  
We consider some constructions of perfect binary codes with the purpose to outline bounds on the number of nonequivalent perfect binary codes and we present the best known lower and upper bounds on the  ...  number of di erent perfect binary codes.  ...  In 1996 Avgustinovich and Solov'eva [3] gave a construction of perfect codes which led to a new lower bound on the number of di erent perfect codes.  ... 
doi:10.1016/s0012-365x(99)00188-0 fatcat:u7ndxiyxlff65cpjlrwfhh3xam
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