Duursma's reduced polynomial
Information Theory
2015-05-11 v1 Algebraic Geometry
math.IT
Abstract
The weight distribution of a linear code C is put in an explicit bijective correspondence with Duursma's reduced polynomial of C. We prove that the Riemann Hypothesis Analogue for a linear code C requires the formal self-duality of C and imposes an upper bound on the cardinality q of the basic field, depending on the dimension and the minimum distance of C. Duursma's reduced polynomial of the function field of a curve X of genus g over the field with q elements is shown to provide a generating function for the numbers of the effective divisors of non-negative degree degree of a virtual function field of a curve of genus g-1 over the same finite field.
Keywords
Cite
@article{arxiv.1505.01993,
title = {Duursma's reduced polynomial},
author = {Azniv Kasparian and Ivan Marinov},
journal= {arXiv preprint arXiv:1505.01993},
year = {2015}
}