On linear codes
Date of Publication
2002
Document Type
Bachelor's Thesis
Degree Name
Bachelor of Science in Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Abstract/Summary
This study is an exposition of Chapter 5 of the book entitled Elements of Algebraic Coding Theory by Lekh Vermani [7]. This paper studies the properties of linear codes over the binary field. A linear binary code is a kind of code defined as the set of all linear combinations of a number of independent vectors over the binary field. The thesis discusses how to generate linear codes using matrices. The concept of dual codes will be introduced and consequently, self-duality of binary linear codes will be given emphasis. The weight enumerator of a code gives information about the weight distribution of a code, i. e. given the weight enumerator, one should be able to know the number of code words given a specific weight. Weight enumerators and one of the most important theorem about weight enumerators, the Mac Williams' formula will be discussed in detail. Examples in obtaining new codes from a given code shall be provided in the paper.
Abstract Format
html
Language
English
Format
Accession Number
TU11100
Shelf Location
Archives, The Learning Commons, 12F, Henry Sy Sr. Hall
Physical Description
84 numb. leaves
Recommended Citation
De Leon, M. R., & Lim, M. C. (2002). On linear codes. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/17232
