Canonical Representation of Quasicyclic Codes Using Gröbner Bases Theory

Kristine Lally ()
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Kristine Lally: RMIT University, Department of Mathematics

A chapter in Gröbner Bases, Coding, and Cryptography, 2009, pp 351-355 from Springer

Abstract: Abstract The tools and techniques of Gröbner bases theory have proved useful in characterising quasicyclic codes and analysing their algebraic structure. A canonical generating set can be obtained from the reduced Gröbner basis of an associated module structure. The very particular form of this generating set allows straightforward determination of properties such as dimension, in manner directly analogous to the theory developed for cyclic codes.

Keywords: Cyclic Code; Convolutional Code; Dual Code; Parity Check Matrix; Matrix Generator Matrix (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-93806-4_19

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DOI: 10.1007/978-3-540-93806-4_19

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