Comparing permutation codes
Speaker: Dr. Cristina Martinez Ramirez (UCD)
Time: 4.00PM
Date: Monday October 13th 2014
Location: UCD School of Mathematical Sciences Seminar Room, Ag. 1.01
Abstract:
Let C be a smooth projective curve defined over a finite field F_q. To each non-constant rational function on the function field F/F_q of the curve, one can associate a matrix with entries in F_q corresponding to the matrix of an endomorphism of F_q-modules. Algebraic geometric codes are constructed by evaluating this rational function over a set of distinct places {p_1, ...., p_n} of F/F_q. In particular when p_1,...,p_n are of degree 1 these are known as Goppa codes. Here we will concentrate on the case of cyclic codes also known as Reed-Solomon (RS) codes which are constructed by evaluating a rational function over a divisor supported on a set of rational places, for example a basis of the underlying vector space (F_q)^{n}. Furthermore, we consider families of permutation codes obtained by applying to a given RS code a permutation matrix in the general linear group GL(n,F_q). This problem is also related with the representation theory of GL(n, F_q) and the construction of t-designs.
Series: UCD Algebra and Number Theory
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