Title :
On the splitting of places in a tower of function fields meeting the Drinfeld-Vladut bound
Author :
Aleshnikov, Ilia ; Kumar, P. Vijay ; Shum, Kenneth W. ; Stichtenoth, Henning
Author_Institution :
Univ. Gesamthochschule Essen, Germany
fDate :
5/1/2001 12:00:00 AM
Abstract :
A description of how places split in an asymptotically optimal tower of function fields studied by Garcia and Stichtenoth (1995) is provided and an exact count of the number of places of degree one is given. This information is useful in the setting up of generator matrices for algebraic-geometry codes constructed over this function field tower. These long codes have performance that asymptotically improves upon the Gilbert-Varshamov bound
Keywords :
algebraic geometric codes; matrix algebra; Drinfeld-Vladut bound; Gilbert-Varshamov bound; algebraic-geometry codes; asymptotically optimal tower; function field tower; function fields; generator matrices; long codes; places splitting; Codes; Cryptography; Decoding; Equations; Galois fields; Interpolation; Linear systems; Notice of Violation; Poles and towers; Polynomials;
Journal_Title :
Information Theory, IEEE Transactions on
