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Linear Block Codes

  • Orhan GaziEmail author
Chapter

Abstract

In this chapter, we will explain the construction of linear block codes. Since linear block codes are vector subspaces, we advise to the reader to study Chap.  1 before proceeding to Chap.  2. Without the knowledge of basic concepts of linear algebra, such as groups, fields, vector spaces, and subspaces, it is difficult to comprehend the philosophy behind the concept of linear block codes. We advise the reader to study the section related to the philosophy of channel encoding before studying the sections related to the encoding and decoding operations. We explain the purpose of channel encoding in Sect. 2.5. After introducing the construction of linear block codes, we explain the encoding operation and give some fundamental definitions such as minimum distance, generator matrix, and parity check matrix. In sequel, we explain equivalent codes, error detection and correction capability of linear block codes, and Hamming spheres.

Keywords

Generator matrix Parity check matrix Encoding Hamming spheres Error correction Error detection 

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Electronic & Communication Engineering DepartmentCankaya UniversityAnkaraTurkey

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