Linear and circular single‐change covering designs revisited

Abstract

AbstractA single‐change covering design (SCCD) is a ‐set and an ordered list of blocks of size where every pair from must occur in at least one block. Each pair of consecutive blocks differs by exactly one element. This is a linear single‐change covering design, or more simply, a single‐change covering design. A single‐change covering design is circular when the first and last blocks also differ by one element. A single‐change covering design is minimum if no other smaller design can be constructed for a given . In this paper, we use a new recursive construction to solve the existence of circular SCCD() for all and three residue classes of circular SCCD() modulo 16. We solve the existence of three residue classes of SCCD modulo 16. We prove the existence of circular SCCD, for all , using difference methods.