# coding theory

Published articles for coding theory.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## The Codes of Solomon, Reed, and Muller

DevFeed: [The Codes of Solomon, Reed, and Muller](<https://devfeed.tech/articles/the-codes-of-solomon-reed-and-muller-40380.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2015/03/23/the-codes-of-solomon-reed-and-muller/>)

Published: 2015-03-23T09:00:00Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Code](<https://devfeed.tech/topics/code.md>), [Decoding](<https://devfeed.tech/topics/decoding.md>)

Tags: [code](<https://devfeed.tech/tags/code.md>), [coding-theory](<https://devfeed.tech/tags/coding-theory.md>), [decoding](<https://devfeed.tech/tags/decoding.md>), [hamming-code](<https://devfeed.tech/tags/hamming-code.md>), [information-theory](<https://devfeed.tech/tags/information-theory.md>), [linear-codes](<https://devfeed.tech/tags/linear-codes.md>), [projection](<https://devfeed.tech/tags/projection.md>), [reed-muller-code](<https://devfeed.tech/tags/reed-muller-code.md>), [reed-solomon-code](<https://devfeed.tech/tags/reed-solomon-code.md>)

### AI overview

This article introduces Reed-Solomon codes, explains the Singleton bound for codes with parameters (n,k,d)q, proves the bound using a projection map, and relates codes that meet the bound to maximum distance separable codes. It also places Reed-Muller codes in the broader discussion.

### Source excerpt

Last time we defined the Hamming code. We also saw that it meets the Hamming bound, which is a measure of how densely a code can be packed inside an ambient space and still maintain a given distance. This time we'll define the Reed-Solomon code which optimizes a different bound called the Singleton bound, and then generalize them to a larger class of codes called Reed-Muller codes. In future posts we'll consider algorithmic issues behind decoding the codes, for now we just care about their existence and optimality properties.

## Hamming's Code

DevFeed: [Hamming's Code](<https://devfeed.tech/articles/hamming-s-code-40378.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2015/03/02/hammings-code/>)

Published: 2015-03-02T09:00:00Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Code](<https://devfeed.tech/topics/code.md>), [Encoding](<https://devfeed.tech/topics/encoding.md>), [digital](<https://devfeed.tech/topics/digital.md>)

Tags: [coding-theory](<https://devfeed.tech/tags/coding-theory.md>), [compression](<https://devfeed.tech/tags/compression.md>), [computing](<https://devfeed.tech/tags/computing.md>), [encoding](<https://devfeed.tech/tags/encoding.md>), [error](<https://devfeed.tech/tags/error.md>), [errors](<https://devfeed.tech/tags/errors.md>), [finite-fields](<https://devfeed.tech/tags/finite-fields.md>), [hamming](<https://devfeed.tech/tags/hamming.md>), [hamming-code](<https://devfeed.tech/tags/hamming-code.md>), [hypercube](<https://devfeed.tech/tags/hypercube.md>), [information-theory](<https://devfeed.tech/tags/information-theory.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [linear-codes](<https://devfeed.tech/tags/linear-codes.md>), [np-hard](<https://devfeed.tech/tags/np-hard.md>), [reed-solomon-codes](<https://devfeed.tech/tags/reed-solomon-codes.md>), [solved](<https://devfeed.tech/tags/solved.md>), [transmission](<https://devfeed.tech/tags/transmission.md>)

### AI overview

This tutorial introduces Hamming codes as efficiently computable encoding schemes for detecting and correcting errors caused by noise during digital transmission. It defines a code as a subset of binary strings and relates codewords to an injective encoding function.

### Source excerpt

Or how to detect and correct errors Last time we made a quick tour through the main theorems of Claude Shannon, which essentially solved the following two problems about communicating over a digital channel. What is the best encoding for information when you are guaranteed that your communication channel is error free? Are there any encoding schemes that can recover from random noise introduced during transmission? The answers to these questions were purely mathematical theorems, of course.

## A Proofless Introduction to Information Theory

DevFeed: [A Proofless Introduction to Information Theory](<https://devfeed.tech/articles/a-proofless-introduction-to-information-theory-40377.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2015/02/16/a-proofless-introduction-to-information-theory/>)

Published: 2015-02-16T09:00:00Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Encoding](<https://devfeed.tech/topics/encoding.md>), [digital](<https://devfeed.tech/topics/digital.md>)

Tags: [channel](<https://devfeed.tech/tags/channel.md>), [coding-theory](<https://devfeed.tech/tags/coding-theory.md>), [communication](<https://devfeed.tech/tags/communication.md>), [compression](<https://devfeed.tech/tags/compression.md>), [digital](<https://devfeed.tech/tags/digital.md>), [encoding](<https://devfeed.tech/tags/encoding.md>), [entropy](<https://devfeed.tech/tags/entropy.md>), [error](<https://devfeed.tech/tags/error.md>), [error-correction](<https://devfeed.tech/tags/error-correction.md>), [example](<https://devfeed.tech/tags/example.md>), [explain](<https://devfeed.tech/tags/explain.md>), [hamming](<https://devfeed.tech/tags/hamming.md>), [independent](<https://devfeed.tech/tags/independent.md>), [information](<https://devfeed.tech/tags/information.md>), [information-theory](<https://devfeed.tech/tags/information-theory.md>), [kolmogorov-complexity](<https://devfeed.tech/tags/kolmogorov-complexity.md>), [language](<https://devfeed.tech/tags/language.md>), [markov](<https://devfeed.tech/tags/markov.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [messages](<https://devfeed.tech/tags/messages.md>), [models](<https://devfeed.tech/tags/models.md>), [probabilistic-method](<https://devfeed.tech/tags/probabilistic-method.md>), [problems](<https://devfeed.tech/tags/problems.md>), [shannon](<https://devfeed.tech/tags/shannon.md>), [theory](<https://devfeed.tech/tags/theory.md>)

### AI overview

A proofless introduction to information theory explains noiseless and noisy communication problems, encoding schemes, entropy, and how entropy differs from Kolmogorov complexity.

### Source excerpt

There are two basic problems in information theory that are very easy to explain. Two people, Alice and Bob, want to communicate over a digital channel over some long period of time, and they know the probability that certain messages will be sent ahead of time. For example, English language sentences are more likely than gibberish, and "Hi" is much more likely than "asphyxiation." The problems are: Say communication is very expensive.