On the algebraic structure of quasi-cyclic codes IV : repeated roots

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...

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Bibliographic Details
Main Authors: Ling, San, Niederreiter, Harald, Sole, Patrick
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2013
Subjects:
DRNTU::Engineering::Computer science and engineering::Computing methodologies::Symbolic and algebraic manipulation
Online Access:https://hdl.handle.net/10356/96413
http://hdl.handle.net/10220/9841
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Institution: Nanyang Technological University
Language: English
Description
Summary: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.

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