Abstract
In this work, we study a family of self-dual four circulant codes and a family of self-dual four negacirculant codes, and the exact counting formula is derived for these families of codes. In addition, we prove that asymptotically good self-dual four circulant codes and negacirculant codes over finite fields exist, and both of them satisfy a modified Gilbert-Varshamov bound on the relative minimum distance with asymptotic rate 12.
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