Some results on free Euclidean self-dual codes over F2+vF2

Abstract

 In this paper, free Euclidean self-dual codes over the ring  F₂ + v F₂  with v² =v 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 + v F₂  to F₂ x  F₂, the generator matrix of the binary code which corresponds the code over the ring F₂ + v F₂  is obtained. The codes of lengths up to 100 over the ring F₂ + v F₂ are found.

Keywords

• Euclidean self-dual codes,codes over rings,Chinese remainder theorem

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