Some results on free Euclidean self-dual codes over 𝔽𝟐 + 𝝊𝔽𝟐

Özet

In this paper, free Euclidean self-dual codes over the ring 𝔽2 + 𝜐𝔽2 with 𝜐2 = 𝜐 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 𝔽2 + 𝜐𝔽2 to 𝔽2 × 𝔽2, the generator matrix of the binary code which corresponds the code over the ring 𝔽2 + 𝜐𝔽2 is obtained. The codes of lengths up to 100 over the ring 𝔽2 + 𝜐𝔽2 are found.