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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Dean Crnković & Ana Grbac, 2024. "Self-Dual and LCD Codes from Kneser Graphs K( n , 2) and Generalized Quadrangles," Mathematics, MDPI, vol. 12(23), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3795-:d:1533924
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    References listed on IDEAS

    as
    1. Stefka Bouyuklieva & Javier de la Cruz & Darwin Villar, 2022. "Extremal Binary and Ternary Codes of Length 60 with an Automorphism of Order 29 and a Generalization," Mathematics, MDPI, vol. 10(5), pages 1-14, February.
    2. Adel N. Alahmadi & Husain S. Alhazmi & Hatoon Shoaib & David G. Glynn & Saeed Ur Rehman & Patrick Solé, 2023. "Connections between Linear Complementary Dual Codes, Permanents and Geometry," Mathematics, MDPI, vol. 11(12), pages 1-11, June.
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