Duursma's reduced polynomial

Azniv Kasparian; Ivan Marinov

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arXiv · 1505.01993

Duursma's reduced polynomial

Azniv Kasparian·Ivan Marinov

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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.

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Azniv Kasparian, Ivan Marinov. 2015-05-08. Duursma's reduced polynomial. https://arxiv.org/abs/1505.01993

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