Concise Encyclopedia of Coding Theory

Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry.

Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references.

The book is divided into three parts:

Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds

Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs

Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography.

Features

• Suitable for students and researchers in a wide range of mathematical disciplines
• Contains many examples and references
• Most topics take the reader to the frontiers of research

大多數編碼理論專家將該領域的起源追溯到1948年克勞德·香農（Claude Shannon）發表的《通信的數學理論》一書。自那時以來，編碼理論已發展成一門具有許多實際應用（天線、網絡、記憶體）的學科，需要各種數學技巧，從交換代數到半定規劃，再到代數幾何。

《編碼理論簡明百科全書》涵蓋的大多數主題以簡短的部分介紹，從入門級別逐漸深入，包含定義、示例和許多參考資料。

該書分為三個部分：
第一部分基礎知識：循環碼、斜循環碼、拟循環碼、自對偶碼、碼和設計、環上的碼、卷積碼、性能界限
第二部分族群：AG碼、群代數碼、少權重碼、布爾函數碼、圖上的碼
第三部分應用：替代度量、算法技術、插值解碼、偽隨機序列、格子、量子編碼、時空碼、網絡編碼、分散存儲、秘密共享和基於碼的加密。

特點：
- 適合各種數學學科的學生和研究人員
- 包含許多示例和參考資料
- 大多數主題將讀者帶到研究的前沿

W. Cary Huffman (1948-) received his PhD in mathematics from the California Institute of Technology in 1974. He taught at Dartmouth College (1974 - 1976) as a John Wesley Young Research Instructor and then at Union College (1976 - 1978). In 1978, he joined the Department of Mathematics and Statistics at Loyola University Chicago, continuing there until his retirement in 2018; he is now professor emeritus. He served as that department's chair from 1986 to 1992. He is co-editor of the Handbook of Coding Theory and co-author of Fundamentals of Error-Correcting Codes, both with Vera Pless. In addition, he has published numerous papers in finite group theory, combinatorics, and algebraic coding theory.

Jon-Lark Kim received his Ph.D. in 2002 from Department of Math of the University of Illinois at Chicago. He was an Associate Professor at the University of Louisville until 2012. He is currently professor at Math Department of Sogang University in Seoul. He has authored more than fifty research papers and one book on Coding Theory. He is the recipient of the 2004 Kirkman medal from the Institute of Combinatorics and its Applications. His research interests include Coding Theory, Cryptography, Combinatorics, Bioinformatics, and Artificial Intelligence.

Patrick Solé (1960-) received the Ingénieur and the Docteur Ingénieur degrees from Ecole Nationale Supérieure des Télécommunications, Paris, France in 1984 and 1987, respectively, and the Habilitation à Diriger des Recherches degree from University of Nice Sophia-Antipolis, France, in 1993.

He has held several visiting positions at Syracuse University, Syracuse, NY, in 1987 - 1989, Macquarie University, Sydney, Australia, in 1994 - 1996, and at University des Sciences et Techniques de Lille, Lille, France, in 1999 - 2000. He has been a permanent member of Centre National de la Recherche Scientifique since 1989 and was later promoted to the rank of Senior Researcher (Directeur de Recherche) in 1996.

His research interests include coding theory (covering radius, codes over rings, geometric codes, quantum codes), interconnection networks (graph spectra, expanders), space time codes (lattices, theta series), and cryptography (Boolean functions, secret sharing schemes).

He is the author of more than 200 journal papers, and of four books.

W. Cary Huffman（1948年-）於1974年從加州理工學院獲得數學博士學位。他曾在達特茅斯學院（1974年-1976年）擔任約翰·韋斯利·楊研究講師，然後在尤宁學院（1976年-1978年）任教。1978年，他加入了芝加哥洛約拉大學的數學與統計學系，一直任教到2018年退休，現為名譽教授。他曾擔任該系主任（1986年至1992年）。他是《編碼理論手冊》的共同編輯，與Vera Pless合著了《錯誤更正碼基礎》。此外，他在有限群理論、組合數學和代數編碼理論等領域發表了許多論文。

Jon-Lark Kim於2002年從伊利諾伊大學芝加哥分校數學系獲得博士學位。他曾任職於路易斯維爾大學的副教授，直到2012年。他目前是首爾蘇岡大學數學系的教授。他撰寫了五十多篇研究論文和一本關於編碼理論的書籍。他獲得了2004年由組合數學與應用研究所頒發的Kirkman獎章。他的研究興趣包括編碼理論、密碼學、組合數學、生物信息學和人工智能。

Patrick Solé（1960年-）於1984年和1987年分別從法國巴黎高等電信學院獲得工程師和博士工程師學位，並於1993年從尼斯索菲亞大學獲得研究指導資格（Habilitation à Diriger des Recherches）學位。

他曾在1987年至1989年間在紐約州雪城大學、1994年至1996年間在悉尼的麥覺理大學以及1999年至2000年間在法國里爾的里爾科學技術大學擔任訪問學者。自1989年以來，他一直是法國國家科學研究中心的常駐成員，並於1996年晉升為高級研究員（Directeur de Recherche）。

他的研究興趣包括編碼理論（覆蓋半徑、環上的編碼、幾何編碼、量子編碼）、互連網絡（圖譜、擴展器）、時空編碼（格子、theta序列）和密碼學（布爾函數、秘密分享方案）。

他是200多篇期刊論文和四本書的作者。