Geodesic
Regular simplex inscribed into a cube, half-circulant Hadamard matrices and Gaussian sums
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 1, pp. 58-81 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved with help of trigonometric sums method that if a number $2n-1$ is prime or equal to product of two prime twin numbers then a half-circulant Hadamard matrix of order $4n$ exists and into a $(4n-1)$-cube one can inscribe a regular simplex of the same dimensions. Group properties of polinomial pairs which give Hadamard matrices of half-circulant type is investigated as well, and it's installed effective necessary existence conditions for a given polinomial (from a group ring over whole numbers) another polinomial which forms with it such the pair what makes use for practical construction of Hadamard matrices of all orders $4n\leq 80$ with help of PC. 
@article{JMAG_2001_8_1_a3,
     author = {A. I. Medianik},
     title = {Regular simplex inscribed into a cube, half-circulant {Hadamard} matrices and {Gaussian} sums},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {58--81},
     year = {2001},
     volume = {8},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2001_8_1_a3/}
}
TY  - JOUR
AU  - A. I. Medianik
TI  - Regular simplex inscribed into a cube, half-circulant Hadamard matrices and Gaussian sums
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2001
SP  - 58
EP  - 81
VL  - 8
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JMAG_2001_8_1_a3/
LA  - ru
ID  - JMAG_2001_8_1_a3
ER  - 
%0 Journal Article
%A A. I. Medianik
%T Regular simplex inscribed into a cube, half-circulant Hadamard matrices and Gaussian sums
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2001
%P 58-81
%V 8
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2001_8_1_a3/
%G ru
%F JMAG_2001_8_1_a3
A. I. Medianik. Regular simplex inscribed into a cube, half-circulant Hadamard matrices and Gaussian sums. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 1, pp. 58-81. http://geodesic.mathdoc.fr/item/JMAG_2001_8_1_a3/