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Linear Block Codes

  • Giuliano Gadioli La GuardiaEmail author
Chapter
  • 38 Downloads
Part of the Quantum Science and Technology book series (QST)

Abstract

As usual, in this chapter we consider that p denotes a prime number, q is a prime power and \({\mathbb F}_{q}\) is the finite field with q elements. We begin by defining the general concept of a code over \({\mathbb F}_{q}\); after this, we present the concept of a linear code that is the more important class of codes in coding and information theory due to its vector space structure. In this subsection, the vectors are written in bold.

Keywords

Generator matrix of a code Parity check matrix of a code Hamming distance Minimum distance of a linear code Euclidean dual code Hermitian dual code Code extension Code expansion Punctured code Direct sum of codes Direct product of codes The (u | u \(+\) v) construction Cyclic codes BCH codes Algebraic geometry codes. 

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsPonta Grossa State UniversityPonta GrossaBrazil

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