Some results on free Euclidean self-dual codes over ?? + ???

In this paper, free Euclidean self-dual codes over the ring ?2 + ??2 with ?2 = ? of order 4 are considered. A necessary and sufficient condition for the form of the generator matrix of a free Euclidean self-dual code is given. By using the distance preserving Gray map from ?2 + ??2 to ?2 × ?2, the generator matrix of the binary code which corresponds the code over the ring ?2 + ??2 is obtained. The codes of lengths up to 100 over the ring ?2 + ??2 are found.

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