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https://hdl.handle.net/10356/96413| Title: | On the algebraic structure of quasi-cyclic codes IV : repeated roots | Authors: | Ling, San Niederreiter, Harald Sole, Patrick |
Keywords: | DRNTU::Engineering::Computer science and engineering::Computing methodologies::Symbolic and algebraic manipulation | Issue Date: | 2006 | Source: | Ling, S., Niederreiter, H., & Solé, P. (2006). On the Algebraic Structure of Quasi-cyclic Codes IV: Repeated Roots. Designs, Codes and Cryptography, 38(3), 337-361. | Series/Report no.: | Designs, codes and cryptography | Abstract: | A trace formula for quasi-cyclic codes over rings of characteristic not coprime with the co-index is derived. The main working tool is the Generalized Discrete Fourier Transform (GDFT), which in turn relies on the Hasse derivative of polynomials. A characterization of Type II self-dual quasi-cyclic codes of singly even co-index over finite fields of even characteristic follows. Implications for generator theory are shown. Explicit expressions for the combinatorial duocubic, duoquintic and duoseptic constructions in characteristic two over finite fields are given. | URI: | https://hdl.handle.net/10356/96413 http://hdl.handle.net/10220/9841 |
DOI: | 10.1007/s10623-005-1431-7 | Schools: | School of Physical and Mathematical Sciences | Rights: | © 2006 Springer Science+Business Media. This is the author created version of a work that has been peer reviewed and accepted for publication by Designs, Codes and Cryptography, Springer Science+Business Media. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1007/s10623-005-1431-7]. | Fulltext Permission: | open | Fulltext Availability: | With Fulltext |
| Appears in Collections: | SPMS Journal Articles |
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| 50. On the algebraic structure of quasi-cyclic codes IV repeated roots.pdf | 288.57 kB | Adobe PDF |  View/Open |
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