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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.
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: [].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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