Figure .
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Infinite families of 2-designs from two classes of binary cyclic codes with three nonzeros
February
2022, 16(1): 169-183.
doi: 10.3934/amc.2020107
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.
Keywords:
Linear codes,
triangular graphs,
permutation decoding,
antiblocking decoding,
antiblocking systems.
Mathematics Subject Classification:
Primary: 94B05, 94B35.
Citation:
Hans-Joachim Kroll, Sayed-Ghahreman Taherian, Rita Vincenti. Optimal antiblocking systems of information sets for the binary codes related to triangular graphs. Advances in Mathematics of Communications,
2022, 16
(1)
: 169-183.
doi: 10.3934/amc.2020107
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References:
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J. D. Key, J. Moori and B. G. Rodrigues,
Permutation decoding for the binary codes from triangular
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H.-J. Kroll and R. Vincenti,
Antiblocking decoding, Discrete Appl. Math., 158 (2010), 1461-1464.
doi: 10.1016/j.dam.2010.04.007. |
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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. |
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V. Pless and W. C. Huffman, Handbook of Coding Theory, Elsevier, Amsterdam, 1998. |
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J. Schönheim,
On Coverings, Pacific J. Math., 14 (1964), 1405-1411.
doi: 10.2140/pjm.1964.14.1405. |
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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. |
| [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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