Group Invariant Weighing Matrices
Ming Ming Tan
TL;DR
This paper explores the existence of group invariant weighing matrices using algebraic methods, extending concepts like multipliers to group rings with cyclotomic integers, and applying field descent and rational idempotents to establish new non-existence results.
Contribution
It introduces an extension of multipliers to group rings with cyclotomic integers and combines algebraic techniques to derive novel non-existence theorems for group invariant matrices.
Findings
New non-existence results for certain group invariant weighing matrices
Extension of multipliers to group rings with cyclotomic integers
Application of field descent and rational idempotents in algebraic combinatorics
Abstract
We investigate the existence problem of group invariant matrices using algebraic approaches. We extend the usual concept of multipliers to group rings with cyclotomic integers as coefficients. This concept is combined with the field descent method and rational idempotents to develop new non-existence results.
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