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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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
2002
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| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/17232 |
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| Institution: | De La Salle University |
| Language: | English |
| 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. |
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