Abstract: We consider codes with generator and parity check matrix being the Hamming distance matrices of weight t vs weight k q-ary words of lengths n. All dimensions and minimum distances of such codes are determined for all k=t+1 any q and n. For the case k\neq t+1,q=3 we show that Hadamard and extended Hamming binary codes as well as some sporadic cases of optimal codes are particular cases of such codes.

Cite: Danilko V.R. , Mogilnykh I.Y.
Some binary codes from Hamming distance matrices
Международная конференция "Мальцевские чтения" 11-15 Nov 2024