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In this paper, we give optimal self-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 using skew-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 codes whose minimum weights are 17 and 19 over GF(5), are constructed for the first time. These codes are derived from skew-Hadamard matrices of order 40 and 44, respectively. Finally, a new [56, 28, 17] self-dual code is constructed over 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. ©2009 AIMS-SDU

Construction of new self-dual codes over $GF(5)$ using skew-Hadamard matrices