- Previous Article
- AMC Home
- This Issue
-
Next Article
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.
| [1] |
Olof Heden, Martin Hessler. On linear equivalence and Phelps codes. Addendum. Advances in Mathematics of Communications, 2011, 5 (3) : 543-546. doi: 10.3934/amc.2011.5.543 |
| [2] |
Luciano Panek, Jerry Anderson Pinheiro, Marcelo Muniz Alves, Marcelo Firer. On perfect poset codes. Advances in Mathematics of Communications, 2020, 14 (3) : 477-489. doi: 10.3934/amc.2020061 |
| [3] |
Olof Heden. The partial order of perfect codes associated to a perfect code. Advances in Mathematics of Communications, 2007, 1 (4) : 399-412. doi: 10.3934/amc.2007.1.399 |
| [4] |
Markku Lehtinen, Baylie Damtie, Petteri Piiroinen, Mikko Orispää. Perfect and almost perfect pulse compression codes for range spread radar targets. Inverse Problems and Imaging, 2009, 3 (3) : 465-486. doi: 10.3934/ipi.2009.3.465 |
| [5] |
B. K. Dass, Namita Sharma, Rashmi Verma. Characterization of extended Hamming and Golay codes as perfect codes in poset block spaces. Advances in Mathematics of Communications, 2018, 12 (4) : 629-639. doi: 10.3934/amc.2018037 |
| [6] |
Olof Heden, Fabio Pasticci, Thomas Westerbäck. On the existence of extended perfect binary codes with trivial symmetry group. Advances in Mathematics of Communications, 2009, 3 (3) : 295-309. doi: 10.3934/amc.2009.3.295 |
| [7] |
Olof Heden, Denis S. Krotov. On the structure of non-full-rank perfect $q$-ary codes. Advances in Mathematics of Communications, 2011, 5 (2) : 149-156. doi: 10.3934/amc.2011.5.149 |
| [8] |
Helena Rifà-Pous, Josep Rifà, Lorena Ronquillo. $\mathbb{Z}_2\mathbb{Z}_4$-additive perfect codes in Steganography. Advances in Mathematics of Communications, 2011, 5 (3) : 425-433. doi: 10.3934/amc.2011.5.425 |
| [9] |
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 |
| [10] |
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 |
| [11] |
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 |
| [12] |
Tomáš Roubíček. Thermodynamics of perfect plasticity. Discrete and Continuous Dynamical Systems - S, 2013, 6 (1) : 193-214. doi: 10.3934/dcdss.2013.6.193 |
| [13] |
Pavel Bachurin, Konstantin Khanin, Jens Marklof, Alexander Plakhov. Perfect retroreflectors and billiard dynamics. Journal of Modern Dynamics, 2011, 5 (1) : 33-48. doi: 10.3934/jmd.2011.5.33 |
| [14] |
Marcela Mejía, J. Urías. An asymptotically perfect pseudorandom generator. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 115-126. doi: 10.3934/dcds.2001.7.115 |
| [15] |
Rich Stankewitz, Toshiyuki Sugawa, Hiroki Sumi. Hereditarily non uniformly perfect sets. Discrete and Continuous Dynamical Systems - S, 2019, 12 (8) : 2391-2402. doi: 10.3934/dcdss.2019150 |
| [16] |
Yang Yang, Xiaohu Tang, Guang Gong. New almost perfect, odd perfect, and perfect sequences from difference balanced functions with d-form property. Advances in Mathematics of Communications, 2017, 11 (1) : 67-76. doi: 10.3934/amc.2017002 |
| [17] |
A. V. Borisov, I.S. Mamaev, S. M. Ramodanov. Dynamics of two interacting circular cylinders in perfect fluid. Discrete and Continuous Dynamical Systems, 2007, 19 (2) : 235-253. doi: 10.3934/dcds.2007.19.235 |
| [18] |
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 |
| [19] |
Mathieu Dutour Sikiric, Achill Schurmann and Frank Vallentin. Classification of eight-dimensional perfect forms. Electronic Research Announcements, 2007, 13: 21-32. |
| [20] |
Cesare Tronci. Hybrid models for perfect complex fluids with multipolar interactions. Journal of Geometric Mechanics, 2012, 4 (3) : 333-363. doi: 10.3934/jgm.2012.4.333 |
2021 Impact Factor: 1.015
Tools
Metrics
Other articles
by authors
[Back to Top]