A Note on an Asymptotically Good Tame Tower
Siman Yang
TL;DR
This paper analyzes the asymptotic properties of a specific algebraic function field tower, contributing to the construction of algebraic-geometric codes with many rational points.
Contribution
It determines the limit of a particular Kummer tower, expanding understanding of asymptotically good towers over non-prime fields.
Findings
Established the limit of a new Kummer tower
Enhanced knowledge of asymptotic behavior of function field towers
Supported development of better algebraic-geometric codes
Abstract
The explicit construction of function fields tower with many rational points relative to the genus in the tower play a key role for the construction of asymptotically good algebraic-geometric codes. In 1997 Garcia, Stichtenoth and Thomas [6] exhibited two recursive asymptotically good Kummer towers over any non-prime field. Wulftange determined the limit of one tower in his PhD thesis [13]. In this paper we determine the limit of another tower [14].
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Taxonomy
TopicsCoding theory and cryptography · Algebraic Geometry and Number Theory · graph theory and CDMA systems