Structure of group invariant weighing matrices of small weight

• Main Authors: Leung, Ka Hin, Schmidt, Bernhard
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2018
• Subjects: Smith Normal Form; Unique Differences
• Online Access: https://hdl.handle.net/10356/87721; http://hdl.handle.net/10220/44477
• Institution: Nanyang Technological University

We show that every weighing matrix of weight n invariant under a finite abelian group G can be generated from a subgroup H of G with |H|≤2^(n−1). Furthermore, if n is an odd prime power and a proper circulant weighing matrix of weight n and order v exists, then v≤2^(n−1). We also obtain a lower boun...