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	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 94: Information and communication, circuits

Introduction

Information and communication includes questions of particular interest to algebraists, especially coding theory (related to linear algebra and finite groups) and encryption (related to number theory and combinatorics). Many topics appropriate to this area can be expressed in graph-theoretic terms, such as network flows and circuit design. Data compression and visualization overlap with statistics.

History

Applications and related fields

Subfields

• 94A: Communication, information, including encryption, compression
• 94B: Theory of error-correcting codes
• 94C: Circuits, networks
• 94D05: Fuzzy sets and logic (in connection with questions of Section 94), See also 03B52, 03E72, 04A72, 28E10

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

De Bruyn, Kristien. "What is information theory?", Bull. Soc. Math. Belg. Sér. B 36 (1984), 215--234. MR86g:94001

Ross Williams has written a Painless Guide to CRC Error Detection Algorithms.

Among the appropriate newsgroups are sci.crypt, sci.electronics.design, and comp.arch.embedded.

Software and tables

Other web sites with this focus

• Here are the AMS and Goettingen resource pages for area 94.

Selected topics at this site

• What type of mathematics is Information Theory?
• Measures of information content of a message.
• Does a given 0-1 vector have all "1"'s consecutive?
• CRC (Cyclic Redundancy Check) efficiency
• Fine-tuning error-correcting codes to detect human errors
• Weight enumeration of Reed-Muller Codes
• What is coding theory?
• The Golay Code and the game of Mogul
• Algorithmic Information Theory as a measure of program-size complexity
• What is Information Theory?
• Kolmogorov complexity of strings of symbols (relative to a fixed universal Turing machine)