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.

1. 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

1. 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

1. 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