Abstract

Coding theory has developed alongside the use of communication. When communicating across a channel, it is inevitable that such pathways of communication be “noisy”. The absence of noise is virtually impossible to attain, thus there is always some sort of interference across the communication channel. This results in messages not always being received as they were originally sent. In order to solve these problems, coding theory developed. It is used both to detect and correct errors in a variety of codes. Coding theory has grown into a discipline affecting all sorts of areas including but not limited to computer science, mathematics, and engineering. The codes can be used for data compression (or source coding), error correction (or channel coding), cryptography and even network coding. Primarily in error correction do we find codes which we are able to transmit quickly, contain many codewords, and also can correct or detect many errors. Within this discipline, a concentration on algebraic coding theory lies with linear codes. There are a variety of different codes discovered within this set of linear codes, including cyclic and constacyclic codes. In this poster presentation, we will discuss the history of coding theory, going in depth with cyclic and constacyclic codes, as well as discussing the many applications and current problems being resolved using algebraic coding theory.

Modified Abstract

When communicating across a channel, it is inevitable that such pathways of communication be “noisy”, thus there is always some sort of interference across the channel. This results in messages not always being received as they were sent. In order to solve these problems, coding theory developed and is used both to detect and correct errors. It is used for data compression, error correction, cryptography and network coding. In error correction, a concentration on algebraic coding theory lies with linear codes, including cyclic and constacyclic codes. In this poster presentation, we will discuss the history of coding theory, going in depth with cyclic and constacyclic codes, as well as discussing applications and current problems being resolved using algebraic coding theory.

Research Category

Computer Science/Mathematics

Primary Author's Major

Mathematics

Mentor #1 Information

Hai Q Dinh, Ph.D.

Presentation Format

Poster

Start Date

March 2016

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Biographical Sketch

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Headshot

Research Area

Algebra | Other Applied Mathematics | Other Mathematics

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Mar 15th, 1:00 PM

Algebraic Coding Theory: Using Cyclic and Constacyclic Codes

Coding theory has developed alongside the use of communication. When communicating across a channel, it is inevitable that such pathways of communication be “noisy”. The absence of noise is virtually impossible to attain, thus there is always some sort of interference across the communication channel. This results in messages not always being received as they were originally sent. In order to solve these problems, coding theory developed. It is used both to detect and correct errors in a variety of codes. Coding theory has grown into a discipline affecting all sorts of areas including but not limited to computer science, mathematics, and engineering. The codes can be used for data compression (or source coding), error correction (or channel coding), cryptography and even network coding. Primarily in error correction do we find codes which we are able to transmit quickly, contain many codewords, and also can correct or detect many errors. Within this discipline, a concentration on algebraic coding theory lies with linear codes. There are a variety of different codes discovered within this set of linear codes, including cyclic and constacyclic codes. In this poster presentation, we will discuss the history of coding theory, going in depth with cyclic and constacyclic codes, as well as discussing the many applications and current problems being resolved using algebraic coding theory.