Further results on 3-spontaneous emission error designs

Abstract

The combinatorial object named t-spontaneous emission error design (t-SEED) was proposed by Beth et al. in 2003 to correct errors caused by quantum jumps. The newly rising category of t-SEEDs contains the classical problem of large sets as a subbranch at the extremal optimal situation. In this article we study carefully the necessary conditions for the existence of a 3-(v,4;m) SEED where v≡5 (mod 6), v≥23 and m=v−7 (the largest possible dimension). By considering the derived designs we determine all possible degeneracy graphs to twenty types (including the empty graph). Then we define triad graphs to investigate these degeneracy graphs. Finally we rule out eighteen of them and reduce the leave of the putative optimal 3-SEED to three concrete types.