If an equidistant linear code exists, then its parameters must satisfy certain relations determined by the Plotkin bound. For each set of possible parameters there actually exists an equidistant linear code with these parameters: its generator matrix is a sequence of parity check matrices of Hamming codes. The generator matrix of every equidistant linear code can be brought to this form by suitably rearranging its columns.
Every equidistant linear code is a sequence of dual Hamming codes / Bonisoli, Arrigo. - In: ARS COMBINATORIA. - ISSN 0381-7032. - STAMPA. - 18:(1984), pp. 181-186.
Every equidistant linear code is a sequence of dual Hamming codes
BONISOLI, Arrigo
1984
Abstract
If an equidistant linear code exists, then its parameters must satisfy certain relations determined by the Plotkin bound. For each set of possible parameters there actually exists an equidistant linear code with these parameters: its generator matrix is a sequence of parity check matrices of Hamming codes. The generator matrix of every equidistant linear code can be brought to this form by suitably rearranging its columns.
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