# Distance-optimal sum-rank codes

This page lists some tables of  the linear distance-optimal sum-rank-metric codes with various lengths   and the matrix size 2\*2. For the constructions of SRM codes, we refer to the following references.

1. Z. Cheng, H. Chen,  C. Xie and C. Ding, Cyclic and negacyclic sum-rank codes, preprint, 2024.  

2. H. Chen, Quasi-perfect and distance-optimal codes sum-rank codes, arXiv:2401.11160, 2024.

3. M. Grassl, <http://www.codetables.de>.

4. **The binary linear distance-optimal** **sum-rank codes with various lengths  and the matrix size 2\*2**

| Block length | dimension\[1] | d\_sr |
| ------------ | ------------- | ----- |
| 3            | 4             | 4     |
| 15           | 4\*12         | 4     |
| 63           | 4\*61         | 4     |
| 255          | 4\*252        | 4     |
| 1023         | 4\*1019       | 4     |
| 4095         | 4\*4090       | 4     |

2. **The q-ary linear distance-optimal sum-rank codes with various lengths  and the matrix size 2\*2**

| q | Block length | dimension\[2] | d\_sr |
| - | ------------ | ------------- | ----- |
| 3 | 80           | 2\*155        | 4     |
| 4 | 255          | 2\*505        | 4     |
| 5 | 624          | 2\*1243       | 4     |
| 7 | 2400         | 2\*4795       | 4     |
| 8 | 4095         | 2\*8185       | 4     |
| 9 | 6560         | 2\*13115      | 4     |

3. **The binary linear distance-optimal** **sum-rank codes with various lengths  and the matrix size 2\*2**

| Block length | dimension\[3] | d\_sr |
| ------------ | ------------- | ----- |
| 11           | 2\*17         | 4     |
| 12           | 2\*19         | 4     |
| 13           | 2\*21         | 4     |
| 14           | 2\*23         | 4     |
| 15           | 2\*25         | 4     |
| 16           | 2\*27         | 4     |
| 17           | 2\*29         | 4     |
| 18           | 2\*30         | 4     |
| 19           | 2\*32         | 4     |
| 20           | 2\*34         | 4     |
| 21           | 2\*36         | 4     |
| 22           | 2\*38         | 4     |
| 23           | 2\*40         | 4     |
| 24           | 2\*42         | 4     |
| 25           | 2\*44         | 4     |
| 26           | 2\*46         | 4     |
| 27           | 2\*48         | 4     |
| 28           | 2\*50         | 4     |
| 29           | 2\*52         | 4     |
| 30           | 2\*54         | 4     |
| 40           | 2\*74         | 4     |
| 50           | 2\*93         | 4     |
| 60           | 2\*113        | 4     |
| 70           | 2\*133        | 4     |
| 80           | 2\*153        | 4     |
| 90           | 2\*173        | 4     |
| 100          | 2\*193        | 4     |
| 110          | 2\*213        | 4     |
| 120          | 2\*233        | 4     |
| 130          | 2\*252        | 4     |