English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper a variety of issues are discussed, Schur ring, $S$-sets,circulant orbits, decimation operator and Hadamard matrices and their relationbetween them is shown. Firstly we define the complete $S$-sets. Next, we studythe structure of Schur ring with circulant basic sets over $\Z_{2}^{n}$ and wedefine the free and non-free circulant $S$-sets, the symmetric, non-symmetricand antisymmetric circulant $S$-sets. We prove that all this $S$-sets areinvariants under decimation. Finally, we prove that if a Hadamard matrix existthen this is contained in a complete $S$-set. Also, we prove that can't existcirculant and with one core Hadamard matrices with some particular structure.These theorems include a result known on symmetric circulant Hadamard matricesof order $4n$ only when $n$ is an odd number.

Schur Ring over Group $\Z_{2}^{n}$, Circulant $S-$Sets Invariant by Decimation and Hadamard Matrices