# Self-orthogonal codes from equitable partitions of association schemes

## TL;DR

This paper presents a method to construct self-orthogonal codes using equitable partitions of association schemes, resulting in optimal codes and introducing self-orthogonal subspace codes with applications to distance-regular graphs.

## Contribution

It introduces a novel construction method for self-orthogonal codes from association schemes and extends the concept to self-orthogonal subspace codes.

## Key findings

- Constructed some optimal self-orthogonal codes.
- Demonstrated the method using distance-regular graphs.
- Proposed a new notion of self-orthogonal subspace codes.

## Abstract

We give a method of constructing self-orthogonal codes from equitable partitions of association schemes. By applying this method we construct self-orthogonal codes from some distance-regular graphs. Some of the obtained codes are optimal. Further, we introduce a notion of self-orthogonal subspace codes. We show that under some conditions equitable partitions of association schemes yield such self-orthogonal subspace codes and we give some examples from distance-regular graphs.