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On finite length nonbinary sequences with large nonlinear complexity over the residue ring $ \mathbb{Z}_{m} $
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New optimal error-correcting codes for crosstalk avoidance in on-chip data buses
Optimal antiblocking systems of information sets for the binary codes related to triangular graphs
1. | Zentrum Mathematik, Technische Universität München, 80290 München, Germany |
2. | Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran |
3. | Dipartimento di Matematica e Informatica Università degli Studi di Perugia, Via Vanvitelli 106123 Perugia, Italy |
We present AI-systems for the binary codes obtained from the adjacency relation of the triangular graphs $ T(n) $ for any $ n\ge 5 $. These AI-systems are optimal and have for $ n $ odd the full error-correcting capability.
References:
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J. D. Key, J. Moori and B. G. Rodrigues,
Permutation decoding for the binary codes from triangular
graphs, European J. Combin., 25 (2004), 113-123.
doi: 10.1016/j.ejc.2003.08.001. |
[2] |
H.-J. Kroll and R. Vincenti,
Antiblocking decoding, Discrete Appl. Math., 158 (2010), 1461-1464.
doi: 10.1016/j.dam.2010.04.007. |
[3] |
H.-J. Kroll and R. Vincenti,
How to find small AI-systems for antiblocking decoding, Discrete Math., 312 (2012), 657-665.
doi: 10.1016/j.disc.2011.06.014. |
[4] |
V. Pless and W. C. Huffman, Handbook of Coding Theory, Elsevier, Amsterdam, 1998. Google Scholar |
[5] |
J. Schönheim,
On Coverings, Pacific J. Math., 14 (1964), 1405-1411.
doi: 10.2140/pjm.1964.14.1405. |
[6] |
V. D. Tonchev, Combinatorial Configurations Designs, Codes, Graphs, Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 40, Longman, New York, 1988. |
show all references
References:
[1] |
J. D. Key, J. Moori and B. G. Rodrigues,
Permutation decoding for the binary codes from triangular
graphs, European J. Combin., 25 (2004), 113-123.
doi: 10.1016/j.ejc.2003.08.001. |
[2] |
H.-J. Kroll and R. Vincenti,
Antiblocking decoding, Discrete Appl. Math., 158 (2010), 1461-1464.
doi: 10.1016/j.dam.2010.04.007. |
[3] |
H.-J. Kroll and R. Vincenti,
How to find small AI-systems for antiblocking decoding, Discrete Math., 312 (2012), 657-665.
doi: 10.1016/j.disc.2011.06.014. |
[4] |
V. Pless and W. C. Huffman, Handbook of Coding Theory, Elsevier, Amsterdam, 1998. Google Scholar |
[5] |
J. Schönheim,
On Coverings, Pacific J. Math., 14 (1964), 1405-1411.
doi: 10.2140/pjm.1964.14.1405. |
[6] |
V. D. Tonchev, Combinatorial Configurations Designs, Codes, Graphs, Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 40, Longman, New York, 1988. |

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