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Bounds and constructions for key distribution schemes
On the existence of extended perfect binary codes with trivial symmetry group
1. | Department of Mathematics, KTH, Stockholm, Sweden S-100 44 |
2. | Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli, 1, I-06123 Perugia, Italy |
3. | Department of Mathematics, KTH, S-100 44 Stockholm, Sweden |
[1] |
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 |
[2] |
Jan J. Sławianowski, Vasyl Kovalchuk, Agnieszka Martens, Barbara Gołubowska, Ewa E. Rożko. Essential nonlinearity implied by symmetry group. Problems of affine invariance in mechanics and physics. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 699-733. doi: 10.3934/dcdsb.2012.17.699 |
[3] |
Olof Heden. A survey of perfect codes. Advances in Mathematics of Communications, 2008, 2 (2) : 223-247. doi: 10.3934/amc.2008.2.223 |
[4] |
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 |
[5] |
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 |
[6] |
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 |
[7] |
Sergio Estrada, J. R. García-Rozas, Justo Peralta, E. Sánchez-García. Group convolutional codes. Advances in Mathematics of Communications, 2008, 2 (1) : 83-94. doi: 10.3934/amc.2008.2.83 |
[8] |
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 |
[9] |
L. Bakker. A reducible representation of the generalized symmetry group of a quasiperiodic flow. Conference Publications, 2003, 2003 (Special) : 68-77. doi: 10.3934/proc.2003.2003.68 |
[10] |
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 |
[11] |
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 |
[12] |
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 |
[13] |
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 |
[14] |
Terasan Niyomsataya, Ali Miri, Monica Nevins. Decoding affine reflection group codes with trellises. Advances in Mathematics of Communications, 2012, 6 (4) : 385-400. doi: 10.3934/amc.2012.6.385 |
[15] |
Jamshid Moori, Amin Saeidi. Some designs and codes invariant under the Tits group. Advances in Mathematics of Communications, 2017, 11 (1) : 77-82. doi: 10.3934/amc.2017003 |
[16] |
Cristina García Pillado, Santos González, Victor Markov, Consuelo Martínez, Alexandr Nechaev. New examples of non-abelian group codes. Advances in Mathematics of Communications, 2016, 10 (1) : 1-10. doi: 10.3934/amc.2016.10.1 |
[17] |
Steven T. Dougherty, Cristina Fernández-Córdoba, Roger Ten-Valls, Bahattin Yildiz. Quaternary group ring codes: Ranks, kernels and self-dual codes. Advances in Mathematics of Communications, 2020, 14 (2) : 319-332. doi: 10.3934/amc.2020023 |
[18] |
Crnković Dean, Vedrana Mikulić Crnković, Bernardo G. Rodrigues. On self-orthogonal designs and codes related to Held's simple group. Advances in Mathematics of Communications, 2018, 12 (3) : 607-628. doi: 10.3934/amc.2018036 |
[19] |
Axel Kohnert, Johannes Zwanzger. New linear codes with prescribed group of automorphisms found by heuristic search. Advances in Mathematics of Communications, 2009, 3 (2) : 157-166. doi: 10.3934/amc.2009.3.157 |
[20] |
Michele Zadra, Elizabeth L. Mansfield. Using Lie group integrators to solve two and higher dimensional variational problems with symmetry. Journal of Computational Dynamics, 2019, 6 (2) : 485-511. doi: 10.3934/jcd.2019025 |
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