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.