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Perfect codes in Euclidean lattices
Computational and Applied Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giselle Strey +2 more
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Involutions in Binary Perfect Codes
IEEE Transactions on Information Theory, 2011Given a 1-perfect code C, the group of symmetries of C, Sym(C)={π ∈ Sn | π(C)=C} , is a subgroup of the group of automorphisms of C. In this paper, we focus on symmetries of order two, i.e., involutions. Let InvF(C) ⊆ Sym(C) be the set of involutions that stabilize F pointwise.
Cristina Fernández-Córdoba +2 more
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IEEE Transactions on Information Theory, 2004
In his pioneering work from 1973, Delsarte conjectured that there are no nontrivial perfect codes in the Johnson scheme. Many attempts were made, during the years which followed, to prove Delsarte's conjecture, but only partial results have been obtained. We survey all these attempts, and prove some new results having the same flavor. We also present a
Tuvi Etzion, Moshe Schwartz 0001
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In his pioneering work from 1973, Delsarte conjectured that there are no nontrivial perfect codes in the Johnson scheme. Many attempts were made, during the years which followed, to prove Delsarte's conjecture, but only partial results have been obtained. We survey all these attempts, and prove some new results having the same flavor. We also present a
Tuvi Etzion, Moshe Schwartz 0001
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On perfect codes for an additive channel
Problems of Information Transmission, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vladimir K. Leont'ev +2 more
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IEEE Transactions on Information Theory, 1998
Summary: We present a few new constructions for perfect linear single byte-correcting codes. These constructions generate some perfect single byte-correcting codes with new parameters, and some perfect single byte-correcting codes with known parameters and simpler presentation and implementation over the known codes. It is also shown that nonequivalent
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Summary: We present a few new constructions for perfect linear single byte-correcting codes. These constructions generate some perfect single byte-correcting codes with new parameters, and some perfect single byte-correcting codes with known parameters and simpler presentation and implementation over the known codes. It is also shown that nonequivalent
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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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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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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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Perfect Multi Deletion Codes Achieve the Asymptotic Optimality of Code Size
IEEE Transactions on Information Theory, 2021Takehiko Mori, Manabu Hagiwara
exaly