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DTSTART:20240310T070000
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DTSTART:20241103T060000
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DTSTART;TZID=America/Toronto:20250210T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-antonina-p-khramova
SUMMARY:Algebraic Graph Theory-Antonina P. Khramova
CLASS:PUBLIC
DESCRIPTION:TITLE: : Algebraic bounds for sum-rank-metric codes\n\nSPEAKER:
 \n Antonina P. Khramova\n\nAFFILIATION:\n Eindhoven University of Technolo
 gy\n\nLOCATION:\n Please contact Sabrina Lato for Zoom link.\n\nABSTRACT
 :The sum-rank metric is a generalization of the well-known\nHamming and ra
 nk metrics. In this talk we introduce two new bounds on\nthe maximal cardi
 nality of the sum-rank-metric code with a given\nminimum distance. One of 
 the bounds exploits a connection between such\na code and a (d-1)-independ
 ent set in a graph defined for the\nsum-rank-metric space. We then use the
  eigenvalues of the graph to\ndeduce the bound. The second bound is derive
 d from the Delsarte's LP\nmethod\, which has been previously obtained for 
 Hamming metric\, rank\nmetric\, Lee metric\, and others\, but the sum-rank
 -metric case remained\nopen. To derive the new LP bound we propose a way t
 o construct an\nassociation scheme for the sum-rank metric\, since the app
 roach used in\nthe Hamming and the rank-metric cases fails due to the asso
 ciated\ngraph not being distance-regular in general. Based on computationa
 l\nexperiments on relatively small instances\, we observe that the\nobtain
 ed bounds often outperform the bounds previously known for\nsum-rank-metri
 c codes.\n\nThis talk is based on a joint work with A. Abiad\, A.L. Gavril
 yuk\, A.\nRavagnani\, and I. Ponomarenko.
DTSTAMP:20260403T082806Z
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