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THE WEIGHT HIERARCHY OF HADAMARD CODES
2019
Facta Universitatis Series Mathematics and Informatics
The support of an $(n, M, d)$ binary code $C$ over the set $\mathbf{A}=\{0,1\}$ is the set of all coordinate positions $i$, such that at least two codewords have distinct entry in coordinate $i$. The $r$th generalized Hamming weight $d_r(C)$, $1\leq r\leq 1+log_2n+1$, of $C$ is defined as the minimum of the cardinalities of the supports of all subset of $C$ of cardinality $2^{r-1}+1$. The sequence $(d_1(C), d_2(C), \ldots, d_k(C))$ is called the Hamming weight hierarchy (HWH) of $C$. In this
doi:10.22190/fumi1904797f
fatcat:lgodlb2b3fhsrfjldg4dgdsdei