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SUMMARY:Mesut Şahin (Hacettepe)
DTSTART:20260327T124000Z
DTEND:20260327T134000Z
DTSTAMP:20260423T052642Z
UID:OBAGS/82
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OBAGS/82/">G
 robner Bases and Linear Codes on Weighted Projective Planes</a>\nby Mesut 
 Şahin (Hacettepe) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n
 \nAbstract\nLet $F$ be the finite field with $q$ elements and $K$ be its a
 lgebraic closure. The ring $S=F[x_0\,x_1\,x_2]$ is graded via $\\deg(x_i)=
 w_i$\, for $i=0\,1\,2$\, where $w_0\, w_1$ and $w_2$ generate a numerical 
 semigroup! We study some linear codes obtained from the weighted projectiv
 e plane $P(w_0\,w_1\,w_2)$ over $K$.\n\nWe get a linear code by evaluating
  homogeneous polynomials of degree $d$  at the subset $Y\\{ P_1\,...\,P_N\
 \}$ of $F$-rational points\, which defines the evaluation map: $f \\mapsto
  (f(P_1)\,...f(P_N))$. The image is a subspace of $F^N$\, which is called 
 a weighted projective Reed-Muller (WPRM) code. Its length is $|Y|=N=q^2+q+
 1$. In the present talk\, we discuss how Grobner theory is used for studyi
 ng the other two parameters: the dimension and the minimum distance extend
 ing and generalizing the results scattered throughout the literature. We a
 lso determine the regularity set which helps eliminating the trivial codes
  as well as giving a lower bound for the minimum distance.\n\nThis is a jo
 int work with Yağmur Çakıroğlu (Hacettepe University) and Jade Nardi (
 Université de Rennes 1).\n
LOCATION:https://researchseminars.org/talk/OBAGS/82/
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