Kernels of nonlinear Hamming codes
Designs, Codes and Cryptography
Nonequivalent q-ary Perfect Codes
SIAM Journal on Discrete Mathematics
Switching Equivalence Classes of Perfect Codes
Designs, Codes and Cryptography
The Mathematical Theory of Coding
The Mathematical Theory of Coding
Construction of Perfect q-ary Codes by Sequential Switchings of \tilde{\alpha}-Components
Problems of Information Transmission
Kernels and p-Kernels of pr-ary 1-Perfect Codes
Designs, Codes and Cryptography
On perfect p-ary codes of length p + 1
Designs, Codes and Cryptography
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The rank of a q-ary code C of length n, r(C), isthe dimension of the subspace spanned by C. We establish the existence of q-ary 1-perfectcodes of length n=\frac {q^m-1}{q-1} for m ≥ 4 and r(C)= n − m + s for each s ∈{1,…,m}. This is a generalization of the binary case proved by Etzion and Vardy in[4].