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On an improved correlation analysis of stream ciphers using multi-output Boolean functions and the related generalized notion of nonlinearity
A survey of perfect codes
| 1. | Department of Mathematics, KTH, Stockholm, Sweden S-100 44 |
This survey paper is devoted to the rather many recent results, that have appeared during the last ten years, on perfect 1-error correcting binary codes. The following topics are considered: Constructions, connections with tilings of groups and with Steiner Triple Systems, enumeration, classification by rank and kernel dimension and by linear equivalence, reconstructions, isometric properties and the automorphism group of perfect codes.
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Xiang Wang, Wenjuan Yin. New nonexistence results on perfect permutation codes under the hamming metric. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021058 |
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Maura B. Paterson, Douglas R. Stinson. Splitting authentication codes with perfect secrecy: New results, constructions and connections with algebraic manipulation detection codes. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021054 |
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Olof Heden, Fabio Pasticci, Thomas Westerbäck. On the symmetry group of extended perfect binary codes of length $n+1$ and rank $n-\log(n+1)+2$. Advances in Mathematics of Communications, 2012, 6 (2) : 121-130. doi: 10.3934/amc.2012.6.121 |
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A. V. Borisov, I.S. Mamaev, S. M. Ramodanov. Dynamics of two interacting circular cylinders in perfect fluid. Discrete & Continuous Dynamical Systems, 2007, 19 (2) : 235-253. doi: 10.3934/dcds.2007.19.235 |
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Yves Edel, Alexander Pott. A new almost perfect nonlinear function which is not quadratic. Advances in Mathematics of Communications, 2009, 3 (1) : 59-81. doi: 10.3934/amc.2009.3.59 |
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Mathieu Dutour Sikiric, Achill Schurmann and Frank Vallentin. Classification of eight-dimensional perfect forms. Electronic Research Announcements, 2007, 13: 21-32. |
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2020 Impact Factor: 0.935
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