1 research outputs found
New Infinite Families of Perfect Quaternion Sequences and Williamson Sequences
We present new constructions for perfect and odd perfect sequences over the
quaternion group . In particular, we show for the first time that perfect
and odd perfect quaternion sequences exist in all lengths for .
In doing so we disprove the quaternionic form of Mow's conjecture that the
longest perfect -sequence that can be constructed from an orthogonal array
construction is of length 64. Furthermore, we use a connection to combinatorial
design theory to prove the existence of a new infinite class of Williamson
sequences, showing that Williamson sequences of length exist for all
when Williamson sequences of odd length exist. Our constructions
explain the abundance of Williamson sequences in lengths that are multiples of
a large power of two.Comment: Version accepted for publicatio