Some Nonexistence and Asymptotic Existence Results for Weighing Matrices
Some Nonexistence and Asymptotic Existence Results for Weighing Matrices
Orthogonal designs and weighing matrices have many applications in areas such as coding theory, cryptography, wireless networking, and communication. In this paper, we first show that if positive integer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math> cannot be written as the sum of three integer squares, then there does not exist any skew-symmetric weighing …