z-logo
Premium
On Skew E–W Matrices
Author(s) -
Armario José Andrés,
Frau María Dolores
Publication year - 2016
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21519
Subject(s) - mathematics , skew , combinatorics , order (exchange) , integer (computer science) , matrix (chemical analysis) , skew symmetric matrix , identity matrix , discrete mathematics , square matrix , symmetric matrix , eigenvalues and eigenvectors , computer science , telecommunications , materials science , physics , finance , quantum mechanics , economics , composite material , programming language
An E–W matrix M is a ( − 1, 1)‐matrix of order 4 t + 2 , where t is a positive integer, satisfying that the absolute value of its determinant attains Ehlich–Wojtas' bound. M is said to be of skew type (or simply skew) if M − I is skew‐symmetric where I is the identity matrix. In this paper, we draw a parallel between skew E–W matrices and skew Hadamard matrices concerning a question about the maximal determinant. As a consequence, a problem posted on Cameron's website [7] has been partially solved. Finally, codes constructed from skew E–W matrices are presented. A necessary and sufficient condition for these codes to be self‐dual is given, and examples are provided for lengths up to 52.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here