Some Explicit Bases Of Riemann-Roch Spaces For Algebraic Geometry Codes
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Date
2011
Authors
Tan, Yean Nee
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
According to Shannon’s Channel Coding Theorem, a code should have long length so that the probability of errors occurring, during the transmission of codewords through a channel, approaches zero. Hence, a good linear code should have long length, large dimension and large minimum distance. The main problem in coding theory is to find optimal linear codes having the largest value of dimension for a given value of length and minimum distance. This problem is equivalent to the problem of finding the largest possible value of information rate for a given value of relative minimum distance. A lower bound on information rate named Tsfasman-Vladut-Zink bound has been found in year 1982 using sequences of algebraic geometry codes (AG codes). Since then, AG code has become an important family of linear codes.
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Keywords
Riemann-Roch Spaces , Algebraic Geometry Codes