Abstract
It is shown that key instruments for composition of four-symbol δ \delta -codes are the Lagrange identity for polynomials, a certain type of quasisymmetric sequences (i.e., a set of normal or near normal sequences) and base sequences. The following is proved: If a set of base sequences for length t t and a set of normal (or near normal) sequences for length n n exist then four-symbol δ \delta -codes of length ( 2 n + 1 ) t ( or n t ) \left ( {2n + 1} \right )t\left ( {{\text {or }}nt} \right ) can be composed by application of the Lagrange identity. Consequently a new infinite family of Hadamard matrices of order 4 u w 4uw can be constructed, where w w is the order of Williamson matrices and u = ( 2 n + 1 ) t ( or n t ) u = \left ( {2n + 1} \right )t\left ( {{\text {or }}nt} \right ) . Other related topics are also discussed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
