Coding Bounds of Linear Network Error Correction Codes

Abstract

AbstractAs far as we know, there are many different types of coding bounds in classical coding theory, which measure the efficiency of a code. Similarly, some important and useful coding bounds in classical coding theory are generalized to linear network error correction coding, including the Hamming bound, the Gilbert-Varshamov bound and the Singleton bound. While the former two bounds are both interesting theoretical results, the Singleton bound plays a very important role in the theory of network error correction. In this chapter, we first discuss the Hamming bound and the Singleton bound in detail. In particular, the LNEC maximum distance separable (MDS) codes, defined as the codes meeting the Singleton bound with equality, are studied in detail due to their optimality. Furthermore, we present several constructive algorithms of LNEC codes, particularly, for LNEC MDS codes, and analyze their performance.KeywordsNetwork Error CorrectionCode BoundariesHamming BoundSingleton BoundClassical Coding TheoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.