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

Please use this identifier to cite or link to this item: https://doi.org/10.1007/s10623-005-1431-7

Title:	On the algebraic structure of quasi-cyclic codes IV: Repeated roots
Authors:	Ling, S. Niederreiter, H. Solé, P.
Keywords:	Codes over rings GDFT Hasse derivative Quasi-cyclic codes Self-dual codes Type II codes
Issue Date:	Mar-2006
Citation:	Ling, S., Niederreiter, H., Solé, P. (2006-03). On the algebraic structure of quasi-cyclic codes IV: Repeated roots. Designs, Codes, and Cryptography 38 (3) : 337-361. ScholarBank@NUS Repository. https://doi.org/10.1007/s10623-005-1431-7
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. © 2006 Springer Science+Business Media, Inc.
Source Title:	Designs, Codes, and Cryptography
URI:	http://scholarbank.nus.edu.sg/handle/10635/103769
ISSN:	09251022
DOI:	10.1007/s10623-005-1431-7
Appears in Collections:	Staff Publications

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