A generalized parity function and its use in the construction of perfect codes
SIAM Journal on Algebraic and Discrete Methods
A Class of Perfect Ternary Constant-Weight Codes
Designs, Codes and Cryptography
On Perfect Ternary Constant Weight Codes
Designs, Codes and Cryptography
Discrete Applied Mathematics
Optimal ternary constant-weight codes of weight four and distance six
IEEE Transactions on Information Theory
Completely reducible super-simple designs with block size four and related super-simple packings
Designs, Codes and Cryptography
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We propose inductive constructions of perfect (n,3;n – 1)3 codes (ternary constant-weight codes of length n and weight n – 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.