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

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 Z2k, 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