Algebraic coding theory is an area of discrete applied mathematics that is concerned (in part) with developing error-control codes and encoding/decoding procedures. Many areas of mathematics are used in coding theory, and we focus on the interplay between algebra and coding theory.
Coding theory - Wikipedia
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage.
The study of error-control codes is called coding theory. This area of discrete applied mathematics includes the study and discovery of various coding schemes that are used to increase the number of errors that can be corrected during data transmission. Coding theory emerged following the …
When information is digital, reliability is critical. Need to understand errors, and correct them. Model noise by probability distribution. ]. Channel transmits bits. With probability 1 − p bit transmitted faithfully, and with probability p bit flipped (independent of all other events). Sender encodes • k bits into n bits.
The mathematical theory of error-correcting codes originated in a paper by Claude Shannon [25] from 1948. A code (or a block code) C of length n over a finite alphabet F q of size q is a subset C of the set Fn q of all n-letter words with components from F q. We refer to the elements of C as words, codewords, or vectors. A code over F q is ...
Coding Theory -- from Wolfram MathWorld
2024年12月18日 · Coding theory, sometimes called algebraic coding theory, deals with the design of error-correcting codes for the reliable transmission of information across noisy channels. It makes use of classical and modern algebraic techniques involving finite fields, group theory, and polynomial algebra.
This paper looks at the algebra of simple error-detecting and error-correcting codes and how algebraic tools can be used to create and understand such codes. Without the probabilistic and combinatorial characteristics of these codes taken into consideration, we rely on a few basic measures of codes to assess their usefulness. Sections 1 and 2
8: Algebraic Coding Theory - Mathematics LibreTexts
Coding theory is an application of algebra that has become increasingly important over the last several decades. When we transmit data, we are concerned about sending a message over a channel that could be affected by “noise.”
Algebraic Coding Theory - World Scientific Publishing Co Pte Ltd
This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory", originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field.
Algebraic Coding Theory - Revised Edition: | Guide books | ACM …
This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory", originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field.