Parameters of BCH codes

The Hong Kong University of Science and Technology
Department of Computer Science and Engineering


PhD Thesis Defence


Title: "Parameters of BCH codes"

By

Mr. Hao LIU


Abstract

The theory of error-correcting codes is a key pillar in modern digital 
communications. By introducing redundancy into codewords, error-correcting 
codes make messages robust against noises in communication channels. In 
1948, Shannon proved that arbitrarily reliable communications are possible 
with the help of error-correcting codes. Thereafter, researchers have been 
exploring proper codes with efficient encoding and decoding algorithms. 
BCH codes are a family of cyclic codes with guaranteed error-correcting 
capabilities and efficient decoding algorithms. They are employed in a 
wide range of applications from satellite communications to solid-state 
drives. However, their dimensions and minimum distances are seldom 
settled.

In this thesis, we investigate the parameters of BCH codes. Dimensions of 
BCH codes with three different lengths are explored in a much larger range 
of defining sets than in the previous literature. For suitable cases, we 
determine the dimensions of BCH codes constructed from every feasible 
defining set within an interval; for other cases, we demonstrate the 
dimensions of those constructed from representative defining sets. For 
minimum distances of BCH codes, we summarized the classic conclusions and 
highlight new families of BCH codes whose true minimum distances can be 
determined by innovative methods. We also provide abundant examples of BCH 
codes with determined parameters, some of which are optimal.


Date:			Monday, 21 May 2018

Time:			2:30pm - 4:30pm

Venue:			Room 5508
 			Lifts 25/26

Chairman:		Prof. Matthew Mckay (ECE)

Committee Members:	Prof. Cunsheng Ding (Supervisor)
 			Prof. Huamin Qu
 			Prof. Ke Yi
 			Prof. Maosheng Xiong (MATH)
 			Prof. Qing Xiang (Math. Sci., U of Delaware)


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