#### Abstract Title

Error Correction in Finite Arbitrary Length Binary Messages

#### Abstract

In this work, we shall investigate error correction in binary messages of finite arbitrary length in order to find the densest packing of codewords, i.e., the most efficient set of codewords. This is an important area of research because of the increasing reliance on digital communications, which are based on binary messages. We build on the work of Richard Hamming who contributed the Hamming distance, which is a method for measuring the difference between two segments, i.e., words, of a message. Our results suggest that for a message of length n, where n is at least 4, there are 2^(n-3) single-error correctable codewords out of 2^n possible words. These results will allow us to make further strides toward finding efficient multiple-error correctable codes in the future.

#### Modified Abstract

In this work, we shall investigate error correction in binary messages of finite arbitrary length in order to find the densest packing of codewords, i.e., the most efficient set of codewords. This is an important area of research because of the increasing reliance on digital communications, which are based on binary messages. We build on the work of Richard Hamming who contributed the Hamming distance, which is a method for measuring the difference between two segments, i.e., words, of a message. Our results suggest that for a message of length n, where n is at least 4, there are 2^(n-3) single-error correctable codewords out of 2^n possible words. These results will allow us to make further strides toward finding efficient multiple-error correctable codes in the future.

#### Research Category

Computer Science/Mathematics

#### Mentor #1 Information

Dr. Donald White

#### Presentation Format

Poster

#### Start Date

March 2016

#### Research Area

Algebra | Discrete Mathematics and Combinatorics | Geometry and Topology | Other Applied Mathematics

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Error Correction in Finite Arbitrary Length Binary Messages

In this work, we shall investigate error correction in binary messages of finite arbitrary length in order to find the densest packing of codewords, i.e., the most efficient set of codewords. This is an important area of research because of the increasing reliance on digital communications, which are based on binary messages. We build on the work of Richard Hamming who contributed the Hamming distance, which is a method for measuring the difference between two segments, i.e., words, of a message. Our results suggest that for a message of length n, where n is at least 4, there are 2^(n-3) single-error correctable codewords out of 2^n possible words. These results will allow us to make further strides toward finding efficient multiple-error correctable codes in the future.