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Perfect Codes in the Johnson Schemes
2006 IEEE Information Theory Workshop, 2006In his pioneering work, from 1973, on algebraic approach to codes in association schemes, Dlesarte has conjectured that there are no nontrivial perfect codes in the Johnson schemes. Many attempts were made during the last 30 years to solve this conjecture.
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Subgroup perfect codes in Cayley sum graphs
Des. Codes Cryptogr., 2020Xuanlong Ma, Min Feng, Kaishun Wang
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IEEE Transactions on Information Theory, 1983
The main lines of a partial proof of the "perfect code theorem" are presented. The relevant part refers to the nonexistence of unknown t -perfect codes over arbitrary alphabets for t \not \in \{1, 2, 6, 8\} . The details of the proof can be found in the author's Ph.D. dissertation at the University of Amsterdam.
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The main lines of a partial proof of the "perfect code theorem" are presented. The relevant part refers to the nonexistence of unknown t -perfect codes over arbitrary alphabets for t \not \in \{1, 2, 6, 8\} . The details of the proof can be found in the author's Ph.D. dissertation at the University of Amsterdam.
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Subgroup total perfect codes in Cayley sum graphs
Designs, Codes and CryptographyXiaomeng Wang +3 more
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Perfect and Quasi-Perfect Codes Under the $l_{p}$ Metric
IEEE Transactions on Information Theory, 2017Zhang Tao, G. Ge
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A note on perfect arithmetic codes
IEEE Trans. Inf. Theory, 1986Summary: Recently \textit{S. Ernvall} [ibid. IT-28, 665-667 (1982; Zbl 0485.94020)] has characterized all the moduli m for which the arithmetic distance induces a metric of \(Z_ m\). This gives us several new classes of moduli for which it is natural to study the properties of arithmetic codes.
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On perfect codes and total perfect codes in Cayley sum graph
Journal of Algebraic CombinatoricsN. Ahanjideh +2 more
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Perfect codes for single balanced adjacent deletions
International Symposium on Information Theory, 2017M. Hagiwara
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Perfect binary codes: constructions, properties, and enumeration
IEEE Transactions on Information Theory, 1994T Etzion, Alexander Vardy
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