# Some new constructions of orthogonal designs

Journal Article

### Abstract

• In this paper we construct $OD(4pq^r(q+1)$; $pq^r$, $pq^r$, $pq^r$,

$pq^r$, $pq^{r+1}$, $pq^{r+1}$, $pq^{r+1}$, $pq^{r+1})$ for each

core order $q \equiv 3 {\rm (mod~4)}$, $r\ge 0$ or $q=1$, $p$ odd,

$p \le 21$ and $p \in \{ 25$, $49 \}$, and $COD(2q^r(q+1)$; $q^r$,

$q^r$, $q^{r+1}$, $q^{r+1})$ for any prime power $q \equiv 1 {\rm (mod~4)}$ (including $q=1$), $r \ge 0$.

• 2013

### Citation

• Xia, T., Seberry, J., Xia, M. & Zhang, S. (2013). Some new constructions of orthogonal designs. Australasian Journal of Combinatorics, 55 121-130.

### Scopus Eid

• 2-s2.0-84875152740

### Ro Full-text Url

• http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3267&context=eispapers

### Ro Metadata Url

• http://ro.uow.edu.au/eispapers/2258

• 9

• 121

• 130

• 55

### Place Of Publication

• http://ajc.maths.uq.edu.au/?page=get_volumes&volume=55

### Abstract

• In this paper we construct $OD(4pq^r(q+1)$; $pq^r$, $pq^r$, $pq^r$,

$pq^r$, $pq^{r+1}$, $pq^{r+1}$, $pq^{r+1}$, $pq^{r+1})$ for each

core order $q \equiv 3 {\rm (mod~4)}$, $r\ge 0$ or $q=1$, $p$ odd,

$p \le 21$ and $p \in \{ 25$, $49 \}$, and $COD(2q^r(q+1)$; $q^r$,

$q^r$, $q^{r+1}$, $q^{r+1})$ for any prime power $q \equiv 1 {\rm (mod~4)}$ (including $q=1$), $r \ge 0$.

• 2013

### Citation

• Xia, T., Seberry, J., Xia, M. & Zhang, S. (2013). Some new constructions of orthogonal designs. Australasian Journal of Combinatorics, 55 121-130.

### Scopus Eid

• 2-s2.0-84875152740

### Ro Full-text Url

• http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3267&context=eispapers

### Ro Metadata Url

• http://ro.uow.edu.au/eispapers/2258

• 9

• 121

• 130

• 55

### Place Of Publication

• http://ajc.maths.uq.edu.au/?page=get_volumes&volume=55