On the algebraic structure of quasi-cyclic codes IV : repeated roots
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...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/96413 http://hdl.handle.net/10220/9841 |
| _version_ | 1824456283156119552 |
|---|---|
| author | Ling, San Niederreiter, Harald Sole, Patrick |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Ling, San Niederreiter, Harald Sole, Patrick |
| author_sort | Ling, San |
| collection | NTU |
| description | 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. |
| first_indexed | 2025-02-19T03:51:38Z |
| format | Journal Article |
| id | ntu-10356/96413 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:51:38Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/964132023-02-28T19:40:21Z On the algebraic structure of quasi-cyclic codes IV : repeated roots Ling, San Niederreiter, Harald Sole, Patrick School of Physical and Mathematical Sciences DRNTU::Engineering::Computer science and engineering::Computing methodologies::Symbolic and algebraic manipulation 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. Accepted version 2013-04-18T09:13:16Z 2019-12-06T19:30:19Z 2013-04-18T09:13:16Z 2019-12-06T19:30:19Z 2006 2006 Journal Article 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. https://hdl.handle.net/10356/96413 http://hdl.handle.net/10220/9841 10.1007/s10623-005-1431-7 en Designs, codes and cryptography © 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]. application/pdf |
| spellingShingle | DRNTU::Engineering::Computer science and engineering::Computing methodologies::Symbolic and algebraic manipulation Ling, San Niederreiter, Harald Sole, Patrick On the algebraic structure of quasi-cyclic codes IV : repeated roots |
| title | On the algebraic structure of quasi-cyclic codes IV : repeated roots |
| title_full | On the algebraic structure of quasi-cyclic codes IV : repeated roots |
| title_fullStr | On the algebraic structure of quasi-cyclic codes IV : repeated roots |
| title_full_unstemmed | On the algebraic structure of quasi-cyclic codes IV : repeated roots |
| title_short | On the algebraic structure of quasi-cyclic codes IV : repeated roots |
| title_sort | on the algebraic structure of quasi cyclic codes iv repeated roots |
| topic | DRNTU::Engineering::Computer science and engineering::Computing methodologies::Symbolic and algebraic manipulation |
| url | https://hdl.handle.net/10356/96413 http://hdl.handle.net/10220/9841 |
| work_keys_str_mv | AT lingsan onthealgebraicstructureofquasicycliccodesivrepeatedroots AT niederreiterharald onthealgebraicstructureofquasicycliccodesivrepeatedroots AT solepatrick onthealgebraicstructureofquasicycliccodesivrepeatedroots |