Non-abelian generalization of cyclic codes.

Title: Non-abelian generalization of cyclic codes.
Identifier: AAI9808000
identifier: 9808000
Creator: Shao, Yiren.
Contributor: Adviser: Richard Tolimieri
Date: 1997
Language: English
Publisher: City University of New York.
Subject: Engineering, Electronics and Electrical | Computer Science
Abstract: Every cyclic code of length n over a field F may be viewed as an ideal of the group algebra FG of the cyclic group G of order n. This observation creates the following generalization: let G be a finite non-abelian group, each left ideal W of the group algebra FG is called a non-abelian code over F. Based on the Clifford's theory of idempotents, algorithms for computing the complete set of primitive orthogonal idempotents for non-abelian groups of the form A {dollar}<{dollar} H (semidirect product), where A is a normal finite abelian group and H is an arbitrary finite group, and algorithms for constructing non-abelian codes by idempotents of non-abelian group algebra are developed. Then non-abelian Dihedral codes are constructed, characteristics of these codes are tested, and specific characterization for non-abelian Dihedral codes in Fourier transform domain is found. Based on these spectral characterization, encoding algorithm and decoding algorithm for non-abelian Dihedral codes are developed.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.