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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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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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Two Families of Optimal Linear Codes and Their Subfield Codes
IEEE Transactions on Information Theory, 2020In this paper, a family of $[{q}^{2}-1, 4, {q}^{2}-{q}-2]$ cyclic codes over ${\mathbb F}_{{q}}$ meeting the Griesmer bound is presented. Their duals are $[{q}^{2}-1,{q}^{2}-5,4]$ almost MDS codes and are optimal with respect to the sphere-packing ...
Ziling Heng, Qiuyan Wang, C. Ding
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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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On Pless symmetry codes, ternary QR codes, and related Hadamard matrices and designs
Designs, Codes and Cryptography, 2021It is proved that a code L ( q ) which is monomially equivalent to the Pless symmetry code C ( q ) of length $$2q+2$$ 2 q + 2 contains the (0,1)-incidence matrix of a Hadamard 3- $$(2q+2,q+1,(q-1)/2)$$ ( 2 q + 2 , q + 1 , ( q - 1 ) / 2 ) design D ( q ...
V. Tonchev
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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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Cryptanalysis of a system based on twisted Reed–Solomon codes
Designs, Codes and Cryptography, 2019Twisted Reed–Solomon (TRS) codes are a family of codes that contains a large number of maximum distance separable codes that are non-equivalent to Reed–Solomon codes. TRS codes were recently proposed as an alternative to Goppa codes for the McEliece code-
Julien Lavauzelle, Julian Renner
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The Equivalence of Certain Harper Codes
Bell System Technical Journal, 1969A 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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Construction of Polar Codes in Rayleigh Fading Channel
IEEE Communications Letters, 2019In this letter, we investigate the effective construction method of the polar codes in the Rayleigh fading channel (RFC) based on the Gaussian approximation (GA) algorithm. For the RFC, two algorithms are proposed to find the equivalent binary input AWGN
Dekun Zhou, K. Niu, Chao Dong
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