## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Foundations of Data Science
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

AMC

In this paper we present a method for constructing
self-orthogonal codes from orbit matrices of $2$-designs
that admit an automorphism group $G$ which acts with
orbit lengths $1$ and $w$, where $w$ divides $|G|$.
This is a generalization of an earlier method proposed
by Tonchev for constructing self-orthogonal codes from
orbit matrices of $2$-designs with a fixed-point-free
automorphism of prime order. As an illustration of our
method we provide a classification of self-orthogonal
codes obtained from the non-fixed parts of the orbit
matrices of the symmetric $2$-$(56,11,2)$ designs,
some symmetric designs $2$-$(71,15,3)$ (and their
residual designs), and some non-symmetric $2$-designs,
namely those with parameters $2$-$(15,3,1)$,
$2$-$(25,4,1)$, $2$-$(37,4,1)$, and $2$-$(45,5,1)$,
respectively with automorphisms of order $p$,
where $p$ is an odd prime. We establish that
the codes with parameters $[10,4,6]_3$ and $[11,4,6]_3$
are optimal two-weight codes. Further, we construct
an optimal binary self-orthogonal $[16,5,8]$ code
from the non-fixed part of the orbit matrix of the
$2$-$(64,8,1)$ design with respect to an automorphism
group of order four.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]