Construction of new self-dual codes over $GF(5)$ using skew-Hadamard matrices
Christos Koukouvinos, Dimitris E. Simos · Advances in Mathematics of Communications · 2009
In this paper, we give optimalself-dual codes over $GF(5)$ for lengths $24$, $40$, $48$ and $56$. In particular,new inequivalent $[48, 24]$ and $[56, 28]$ self-dual codes over $GF(5)$ whose minimum weights are $14$ and $16$, are constructed usingskew-Hadamard matrices of order $24$ and $28$,thus improving the only known quadratic double circulant self-dual codes of length $48$ and $56$.Moreover, $[80, 40]$ and $[88, 44]$ self-dual codeswhose minimum weights are $17$ and $19$ over $GF(5)$, areconstructed for the first time. These codes are derived fromskew-Hadamard matrices of order $40$ and $44$, respectively. Finally, a new $[56, 28, 17]$ self-dual code is constructedover $GF(7)$ having the highest minimum weight among $[56, 28]$ self-dual codes.This new optimal code is constructed from a skew-Hadamard-matrix of order $28$, for the first time.