Biquadratic residues and self-orthogonal 2-sequencings (Q1915717)

Let \(2K_n\) denote the complete multigraph on \(n\) vertices in which each edge has multiplicity two. If \(2K_n\) can be partitioned into Hamiltonian paths such that any two distinct paths have exactly one edge in common, write \(2K_n\to P_n\). The object of this paper is to examine a particular class of such partitions introduced in [\textit{B. A. Anderson} and \textit{P. A. Leonard}, Des. Codes Cryptography 1, No. 2, 149-181 (1991; Zbl 0769.05056)], to which the reader is referred for wider discussion of this and related graph decomposition problems. In particular, attention is paid to constructions of these partitions that are based on self-orthogonal 2-sequencings of the additive groups of finite fields.