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New Infinite Families of Perfect Quaternion Sequences and Williamson Sequences.
- Source :
- IEEE Transactions on Information Theory; Dec2020, Vol. 66 Issue 12, p7739-7751, 13p
- Publication Year :
- 2020
-
Abstract
- We present new constructions for perfect and odd perfect sequences over the quaternion group $Q_{8}$. In particular, we show for the first time that perfect and odd perfect quaternion sequences exist in all lengths $2^{t}$ for $t\geq 0$. In doing so we disprove the quaternionic form of Mow’s conjecture that the longest perfect $Q_{8}$ -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 $2^{t} n$ exist for all $t\geq 0$ when Williamson sequences of odd length $n$ exist. Our constructions explain the abundance of Williamson sequences in lengths that are multiples of a large power of two. [ABSTRACT FROM AUTHOR]
- Subjects :
- QUATERNIONS
ORTHOGONAL arrays
SCIENTIFIC computing
FAMILIES
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 66
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 147291932
- Full Text :
- https://doi.org/10.1109/TIT.2020.3016510