Negacyclic and constacyclic codes over finite chain rings

Dissertant

Abu Dahruj, Faysal Muhammad

Thesis advisor

al-Ashker, Muhammad Mahmud

University

Islamic University

Faculty

Faculty of Science

Department

Department of Mathematics

University Country

Palestine (Gaza Strip)

Degree

Master

Degree Date

2008

English Abstract

The negashift v of Z4n is defined as the permeation of Zn such that v (a0, a1, ...., ai, ...., an−1)= (−an−1, a0, ...., ai, ....an−2) and negacyclic code of length n over Z4 is defined as a subset C of Z4n such that v (C) = C. We prove that the Gray image of a linear negacyclic code over Z4 of length n is a binary distance invariant cyclic code.

We introduce (1 + u)-constacyclic and cyclic codes over the ring R2 = F2 + uF2, and study them by analogy with the Z4 case.

We prove that the Gray image of a linear (1 + u)-constacyclic code over R2 of length n is a binary distance invariant cyclic code.

Also we define a Gray map between codes over R3 = F2 + uF2 + u2F2 and codes over F2.

We prove that the Gray image of a linear (1 − u2)-constacyclic code over R3 of length n is a binary distance invariant linear quasi-cyclic code.

Finally we define a new Gray map between Rk = F2 + uF2 + u2F2 + .

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+ uk−1F2 and F2 (k−1) We prove that the Gray image of a linear (1 − uk−1)-constacyclic code over Rk of length n is a binary distance invariant quasi-cyclic code of order k − 1.

Main Subjects

Mathematics

Topics

• Geometry
• Computer software

No. of Pages

93

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-299459