On linear codes
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 independ...
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oai:animorepository.dlsu.edu.ph:etd_bachelors-177452022-01-27T01:32:25Z On linear codes De Leon, Maria Angelica R. Lim, Maria Cristina C. 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. 2002-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/17232 Bachelor's Theses English Animo Repository |
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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. |
| format |
text |
| author |
De Leon, Maria Angelica R. Lim, Maria Cristina C. |
| spellingShingle |
De Leon, Maria Angelica R. Lim, Maria Cristina C. On linear codes |
| author_facet |
De Leon, Maria Angelica R. Lim, Maria Cristina C. |
| author_sort |
De Leon, Maria Angelica R. |
| title |
On linear codes |
| title_short |
On linear codes |
| title_full |
On linear codes |
| title_fullStr |
On linear codes |
| title_full_unstemmed |
On linear codes |
| title_sort |
on linear codes |
| publisher |
Animo Repository |
| publishDate |
2002 |
| url |
https://animorepository.dlsu.edu.ph/etd_bachelors/17232 |
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1772835163839922176 |