Hermitian Codes

• Main Authors: Yean-Nee Tan, 陳彥霓
• Other Authors: Jing-Yu
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/74021650773976830879

碩士 === 國立臺灣大學 === 數學研究所 === 101 === In 1982, Tsfasman, Vladut and Zink discovered a lower bound for the information rates of linear codes, known as the TVZ Bound, using sequences of algebraic geometry codes (AG codes). This discovery had brought the attention of coding theorists to AG codes. In this correspondence, the Hermitian codes has been study thoroughly, owing to the remarkable properties of Hermitian funciton fields. In fact, the true minimal distance of the classical one-point Hermitian codes has been dertermined in [8]. In this thesis, several families of Hermitian codes are discussed; namely, the classical one-point Hermitian codes, the one-point Hermitian codes supported by a place of degree higher than one, and the multple-point Hermitian codes. The focus of this thesis is laid on the consturction of some good Hermitian codes. Besides that, the existence of some Hermitian codes with parameters improved over the much-studied classical one-point Hermitian codes are also discussed. Last but not least, some concrete examples of Hermitian codes are constructed to show the improvement of parameters over the classical one-point Hermitian codes.