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New code equivalence based on relative generalized Hamming weights [PDF]
Information Sciences, 2011 Code equivalence is a basic concept in coding theory. The well-known theorem by MacWilliams gives a sufficient condition for code equivalence. Recently the MacWilliams theorem has been generalized, by Fan, Liu and Puig, making use of the generalized ...
Zihui Liu, Xin-Wen Wu, Yuan Luo
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On equivalent classes of minimal Abelian codes
Journal of Combinatorial Theory, Series A, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yuan Ren, Dongchun Han
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Group Code Equivalence and Optimum Codes
IRE Transactions on Circuit Theory, 1959This paper describes a search for optimum group codes using the IBM 704 computer. Some theory of the relation. ship between equivalent codes used in narrowing the search is described, and the method of searching is outlined. The newly found optimum codes are listed, along with a number of counter-examples to typical conjectures on binary group codes.
A. B. Fontaine, W. Wesley Peterson
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On the equivalence of linear codes
Applicable Algebra in Engineering, Communication and Computing, 2011The authors consider the problem of equivalence of linear codes, i.e., when they differ by a linear isometry of the Hamming space. In that case, the linear isometry is exactly a monomial transformation. Certain equivalent conditions are derived for this notion of equivalence, based upon properties of the relative codes obtained from the relative ...
Zihui Liu, Zhimin Sun
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Journal of Electronic Imaging, 2014
The representation of images is an active and very important area in image processing and pattern recognition. Therefore, in the literature, different contour codes for binary images have been proposed, such as F4;F8;VCC;3OT, and AF8. These codes have been used in many papers since the first chain code, F8, was introduced by Freeman in 1961.
Hermilo Sánchez-Cruz +1 more
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The representation of images is an active and very important area in image processing and pattern recognition. Therefore, in the literature, different contour codes for binary images have been proposed, such as F4;F8;VCC;3OT, and AF8. These codes have been used in many papers since the first chain code, F8, was introduced by Freeman in 1961.
Hermilo Sánchez-Cruz +1 more
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Coding a and Coding B of the Wisc are Not Equivalent Tasks
Perceptual and Motor Skills, 1978WISC Coding A and Coding B were administered to 50 subjects with minimal brain dysfunction and 75 controls whose ages ranged from 7 yr., 8 mo. and 0 days to 8 yr., 3 mo. and 30 days, with half of each group above 8 and half below. Standard scores showed significant differences between Coding A and Coding B suggesting that the two tasks are nor ...
L, Oettinger, L V, Majovski, R R, Gauch
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Asymptotic Improvements to Provable Algorithms for the Code Equivalence Problem [PDF]
IEEE Transactions on Information TheoryWe present several new provable algorithms for two variants of the code equivalence problem on linear error-correcting codes, the Linear Code Equivalence Problem (LCE) and the Permutation Code Equivalence Problem (PCE).
Jean-François Biasse, Huck Bennett
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Switching Equivalence Classes of Perfect Codes
Designs, Codes and Cryptography, 1999A binary 1-error correcting perfect code is called switching equivalent to the Hamming code (of the same parameters) if there is a sequence of switches (replacing a specially selected set of codewords for another set of words) which leads to the Hamming code. \textit{S. V. Avgustinovich} and \textit{F. I.
Kevin T. Phelps, Mike LeVan
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On the Equivalence of Codes over Finite Rings
Applicable Algebra in Engineering, Communication and Computing, 2004Let \(R\) be a finite (not necessarily commutative) ring with identity. The authors call \(R\) a `left (right) MacWilliams ring' if for each \(n\geq 1\) and linear code \(C \subseteq R^n\), every left (right) isometry \(C\rightarrow R^n\) extends to a monomial transformation of \(R^n\).
Hai Quang Dinh 0001 +1 more
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