Session S29 - Theory and Applications of Coding Theory

Wednesday, July 14, 13:00 ~ 13:25 UTC-3

Algebraic interpretation of the minimum distance of Reed-Muller-type codes

Yuriko Pitones

CIMAT , Mexico   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The minimum distance of Reed-Muller-type codes has an algebraic interpretation, in terms of its associated vanishing ideal $I$ and the Hilbert-Samuel multiplicity of $I$, called the $\delta$-function. In this talk, we present this interpretation and study the asymptotic behavior of the $\delta$-function, in particular, we related the stabilization point, $r$ of $I$ of the $\delta$-function with the Castelnuovo-Mumford regularity of $I$. We see that when generalized the $\delta$-function to graded ideals, the point $r I$ is less than or equal to the Castelnuovo -Mumford regularity of $I$, in particular, this claim holds for F-pure and square free monomial ideals.

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