Self-Dual and LCD Codes from Kneser Graphs K( n, 2) and Generalized Quadrangles

Dean Crnković () and Ana Grbac
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Dean Crnković: Faculty of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000 Rijeka, Croatia
Ana Grbac: Faculty of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000 Rijeka, Croatia

Mathematics, 2024, vol. 12, issue 23, 1-14

Abstract: In this paper, we study self-dual and LCD codes constructed from Kneser graphs K( n , 2) and collinearity graphs of generalized quadrangles using the so-called pure and bordered construction. We determine conditions under which these codes are self-dual or LCD. Further, for the codes over Z 2 k , we give the conditions under which they are Type II. Moreover, we study binary and ternary self-dual and LCD codes from Kneser graphs K( n , 2) and collinearity graphs of generalized quadrangles. Furthermore, from the support designs for certain weights of some of the codes, we construct strongly regular graphs and 3-designs.

Keywords: self-dual code; LCD code; strongly regular graph; block design; Kneser graph; generalized quadrangle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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