Fully comprehensive analysis with illustrative examples tocode upper bounds by Delsarte and by Schrijver

• Main Authors: Zhao-MinLiu, 劉兆敏
• Other Authors: Ruey-Lin Sheu
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/zc8h6w

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 106 === In this thesis, we study the maximum size A(n,d) of a binary code of word length n with minimum distance at least d. The problem is NP-hard and there were two earli- est upper bounds for A(n,d) introduced by Philippe Delsarte in 1973 and Alexander Schrijver in 2005. The former is based on linear programming whereas the latter on semidefinite programming. The purpose of this thesis is to understand the two models via many practical examples to comprehend difficult techniques used in the models and their proofs. We also write computer codes to compare numerical results between Delsarte's bound and Schrijver's bound for word length n〈=18.