In this paper, we construct self-dual codes from a construction that involves 2x2 block circulant matrices, group rings and a reverse circulant matrix. We provide conditions whereby this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2, F2 + uF2 and F4 + uF4. Using extensions, neighbours and neighbours of neighbours, we construct 32 new self-dual codes of length 68.
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