Construction of quasi-cyclic self-dual codes

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2013

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Çomak, Pınar

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Quasi-cyclic and self-dual codes are interesting classes of linear codes. Quasi-cyclic codes are linear codes which takes maximum possible value of minimum distance among the codes with the same length and same dimension. Another class of interesting linear codes is the self-dual codes. Self-dual codes have close connections with group theory, lattice theory and design theory. There has been an active research on the classi fication of self-dual codes over fi nite fi elds and over rings. We study on construction of quasi-cyclic self-dual codes, especially binary cubic ones. With a new algebraic approach, binary quasi-cyclic codes of length 3l over a fi eld are defi ned by the linear codes of length l over the ring F2 XF4. İn this thesis, we improve the result for the cubic self-dual binary codes, by fi nding two new self-dual codes with the algebraic approach.

Subject Keywords

Group theory., Lattice theory., Chinese remainder theorem., Quasi-cyclic codes., Self-dual codes.

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http://etd.lib.metu.edu.tr/upload/12616461/index.pdf
https://hdl.handle.net/11511/23096

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Graduate School of Applied Mathematics, Thesis

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Citation Formats

P. Çomak, “Construction of quasi-cyclic self-dual codes,” M.S. - Master of Science, Middle East Technical University, 2013.