A SURVEY ON EXTENDED CODES OF LINEAR CODES OVER FINITE FIELDS

PhD Qualifying Examination


Title: "A SURVEY ON EXTENDED CODES OF LINEAR CODES OVER FINITE FIELDS"

by

Miss Tingfang CHEN


Abstract:

The construction of linear codes over finite fields with good parameters is one
of the most interesting and fundamental topics in coding theory. This problem
is of particular interest especially if the parameters of the code are
"optimal" in a well-known sense. One method of obtaining new codes from known
linear codes is to extend them. The main goal of investigating extended codes
is to generate codes with new parameters, weight distributions, and new
properties, which may get codes with some interesting applications. The study
of the extended codes also helps in verifying some properties of the original
linear codes. However, the extended codes of linear codes are not well studied
yet. The extended codes of certain families of cyclic codes have been
investigated to some extent, but little is known about their parameters and
properties. There are a very small number of references and results on the
extended codes, and the properties of the extended codes of most linear codes
are open in general, requiring further investigation. In this survey, we
present a comprehensive review of the literature on the extended codes of
linear codes. We discuss the recent results of extended codes of different
families of linear codes and summarize some interesting properties and
applications of them. We also explore the progress of the extension theorems
for linear codes and their applications with various parameters over different
finite fields and highlight some open problems and variations on the theme.


Date:                   Wednesday, 30 August 2023

Time:                   10:00am - 12:00noon

Venue:                  Room 5501
                        Lifts 25/26

Committee Members:      Prof. Cunsheng Ding (Supervisor)
                        Dr. Dimitris Papadopoulos (Chairperson)
                        Dr. Amir Goharshady
                        Dr. Maosheng Xiong (MATH)


**** ALL are Welcome ****