Cameron-Liebler line classes in PG(3,q)

Abstract

This thesis concerns a research on Cameron-Liebler line classes in PG(3,q), which were introduced by Cameron and Liebler in their study of collineation groups of PG(3,q) having equally many orbits on points and lines. These line classes have appeared in different contexts under disguised names such as Boolean degree one functions, regular codes of covering radius one, and tight sets. ☐ In this thesis we construct an infinite family of Cameron-Liebler line classes in PG(3,q) with new parameter x = (q+1)^2/3 for all prime powers q congruent to 2 modulo 3. The examples obtained when q is an odd power of two represent the first infinite family of Cameron-Liebler line classes in PG(3,q), q even. This result is joint work with Tao Feng, Koji Momihara, Morgan Rodgers and Qing Xiang.