Title :
Finding the defining functions for one-point algebraic-geometry codes
Author :
Leonard, Douglas A.
Author_Institution :
Dept. of Discrete & Stat. Sci., Auburn Univ., AL, USA
fDate :
9/1/2001 12:00:00 AM
Abstract :
An iterative algorithm is given for producing the parity-check functions for one-point algebraic-geometry (AG) codes, in particular (but not limited to) those related to the two towers of function fields introduced by Garcia and Stichtenoth (1995). This simple method, based on the linearity of the Qth-power map over FQ, is an alternative to the method of using Laurent series expansions. Examples are given for small values of m with characteristic p=2 for both towers
Keywords :
algebraic geometric codes; functions; iterative methods; Qth-power map; defining functions; iterative algorithm; one-point algebraic-geometry codes; parity-check functions; towers of function fields; Equations; Heart; Iterative algorithms; Linearity; Parity check codes; Poles and towers; Polynomials; Pulp and paper industry;
Journal_Title :
Information Theory, IEEE Transactions on
