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Group Code Equivalence and Optimum Codes

IRE Transactions on Circuit Theory, 1959
This 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, 2011
The 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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Equivalence of chain codes

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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Coding a and Coding B of the Wisc are Not Equivalent Tasks

Perceptual and Motor Skills, 1978
WISC 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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On the Equivalence of Codes over Finite Rings

Applicable Algebra in Engineering, Communication and Computing, 2004
Let \(R\) 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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Switching Equivalence Classes of Perfect Codes

Designs, Codes and Cryptography, 1999
A 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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The Equivalence of Certain Harper Codes

Bell System Technical Journal, 1969
A class of binary encoding algorithms called Harper codes has been studied previously as a means of encoding numbers for transmission over an idealized binary channel. This paper considers a more general and practical transmission system model. For any Harper code, it presents a technique for obtaining the expression for the average absolute numerical ...
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Testing efficiency transfer codes for equivalence

Applied Radiation and Isotopes, 2010
Four general Monte Carlo codes (GEANT3, PENELOPE, MCNP and EGS4) and five dedicated packages for efficiency determination in gamma-ray spectrometry (ANGLE, DETEFF, GESPECOR, ETNA and EFFTRAN) were checked for equivalence by applying them to the calculation of efficiency transfer (ET) factors for a set of well-defined sample parameters, detector ...
T, Vidmar   +14 more
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A code equivalence between streaming network coding and streaming index coding

2017 IEEE International Symposium on Information Theory (ISIT), 2017
We consider a delay-constrained streaming model for zero-error communications and show that under this model, network coding and index coding problems are code equivalent. That is, any streaming network coding instance can be efficiently mapped to a corresponding acyclic streaming index coding instance such that an index code for the latter can be ...
Wong, Ming Fai   +2 more
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