Some Common-Used Codes

Yuqi Guo, Yun Liu and Shoufeng Wang
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Yuqi Guo: Lanzhou University, School of Mathematics and Statistics
Yun Liu: Yuxi Normal University, Department of Mathematics
Shoufeng Wang: Yunnan Normal University, Department of Mathematics

Chapter Chapter 2 in Topics on Combinatorial Semigroups, 2024, pp 27-75 from Springer

Abstract: Abstract The theory of codes takes its origin in the theory of information devised by Shannon in 1950s, which is a branch of theoretical computer science. The algebraic theory of codes, which mainly studies the construction, counting, classification and relations of codes satisfying certain algebraic and combinatorial properties, is closed related to the theory of formal languages, automata and semigroups. Some selected topics on the theory of codes are introduced in this chapter, including the method of defining codes by using dependence systems, the maximality and completeness of codes, and the detailed discussion of some special kinds of codes such as convex codes, semaphore codes and solid codes.

Date: 2024
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DOI: 10.1007/978-981-99-9171-6_2

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