Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/143471
Title: Bilinear forms on finite abelian groups and group-invariant Butson Hadamard matrices
Authors: Duc, Tai Do
Schmidt, Bernhard
Keywords: Science::Mathematics
Issue Date: 2019
Source: Duc, T. D., & Schmidt, B. (2019). Bilinear forms on finite abelian groups and group-invariant Butson Hadamard matrices. Journal of Combinatorial Theory, Series A, 166, 337-351. doi:10.1016/j.jcta.2019.03.002
Journal: Journal of Combinatorial Theory, Series A
Abstract: Let K be a finite abelian group and let exp(K) denote the least common multiple of the orders of the elements of K. A BH(K, h) matrix is a K-invariant |K|×|K| matrix H whose entries are complex hth roots of unity such that HH∗ = |K|I, where H∗ denotes the complex conjugate transpose of H, and I is the identity matrix of order |K|. Let νp(x) denote the p-adic valuation of the integer x. Using bilinear forms on K, we show that a BH(K, h) exists whenever (i) νp(h) ≥ νp(exp(K))/2 for every prime divisor p of |K| and (ii) ν2(h) ≥ 2 if ν2(|K|) is odd and K has a direct factor Z2. Employing the field descent method, we prove that these conditions are necessary for the existence of a BH(K, h) matrix in the case where K is cyclic of prime power order.
URI: https://hdl.handle.net/10356/143471
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2019.03.002
Rights: © 2019 Elsevier Inc. All rights reserved. This paper was published in Journal of Combinatorial Theory, Series A and is made available with permission of Elsevier Inc.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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