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

Year 2019, Volume: 23 Issue: 6, 1131 - 1136, 01.12.2019

Refia Aksoy Fatma Çalışkan

https://doi.org/10.16984/saufenbilder.525606

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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