On the algebraic structure of quasi-cyclic codes I : finite fields

• Main Authors: Ling, San, 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/10356/96416; http://hdl.handle.net/10220/9827
• Institution: Nanyang Technological University

A new algebraic approach to quasi-cyclic codes is introduced. The key idea is to regard a quasi-cyclic code over a field as a linear code over an auxiliary ring. By the use of the Chinese remainder theorem (CRT), or of the discrete Fourier transform (DFT), that ring can be decomposed into a direct p...