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Abstract
We propose inductive constructions of perfect (n,3;n – 1)3 codes (ternary constant-weight codes of lengthn and weightn – 1 with distance 3), which are modifications of constructions of perfect binary codes. The construction yields at least\(2^{2^{n/2 - 2} }\) different perfect (n,3;n – 1)3 codes. To perfect (n,3;n – 1)3 codes, perfect matchings in a binary hypercube without close (at distance 1 or 2 from each other) parallel edges are equivalent.
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Krotov, D.S. Inductive Constructions of Perfect Ternary Constant-Weight Codes with Distance 3.Problems of Information Transmission37, 1–9 (2001). https://doi.org/10.1023/A:1010424208992
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