> For the complete documentation index, see [llms.txt](https://jnu-coding-crypts-organization.gitbook.io/sum-rank-metric-codes/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jnu-coding-crypts-organization.gitbook.io/sum-rank-metric-codes/linear-sum-rank-metric-codes.md). # Linear sum-rank-metric codes This page lists some tables of the dimensions of the linear sum-rank-metric codes with various lengths and the matrix size n\*m. For the constructions of SRM codes, we refer to the following references. 1. U. MartÍnez-Peňas, Sum-rank BCH codes and cyclic-skew-cyclic codes, IEEE Transactions on Information Theory, vol. 67, no. 8, pp. 51495167, 2021. 2. H. Chen, New explicit linear sum-rank-metric codes, IEEE Transactions on Information Theory, vol. 69, no. 10, pp. 6303-6313, 2023. 3. H. Chen, Z. Cheng and Y. Qi, Construction and fast decoding of binary linear sum-rank-metric codes, arXiv:2311.03619, 2023. #### Table 1: Block length t=7, q=2, n=m=2
Minimum sum-rank distanceReference 2Reference 1 (Table III)Singleton-like
22*132*122*13
32*102*92*12
42*92*62*11
52*62*52*10
62*52*52*9
72*42*22*8
#### #### Table 2： Block length t=15, q=2, n=m=2
Minimum sum-rank distanceReference 2Reference 1 (Table IV)Singleton-like
42*252*202*27
52*212*182*26
62*202*162*25
72*182*142*24
82*172*102*23
92*132*82*22
102*132*82*21
112*112*62*20
122*102*42*19
132*8none2*18
142*82*22*17
152*7none2*16
#### Table 3： Block length t=17, q=2, n=m=2
Minimum sum-rank distanceReference 2Singleton-like
42*292*31
52*252*30
62*242*29
72*222*28
82*212*27
92*202*26
102*162*25
112*142*24
122*142*23
132*112*22
142*102*21
152*92*20
162*82*19
172*72*18
#### #### Table 4： Block length t=31, q=2, n=m=2
Minimum sum-rank distanceReference 2Reference 1 (Table V)Singleton-like
42*552*502*59
52*512*472*58
62*502*452*57
72*462*402*56
82*452*352*55
92*41none2*54
102*402*302*53
112*38none2*52
122*382*252*51
132*33none2*50
142*312*202*49
152*29none2*48
162*28none2*47
172*25none2*46
182*242*72*45
192*22none2*44
202*21none2*43
212*19none2*42
222*192*72*41
232*18none2*40
242*17none2*39
252*13none2*38
262*132*22*37
272*12none2*36
282*12none2*35
292*11none2*34
302*112*22*33
#### Table 5： Block length t=63, q=2, n=m=2
Minimum sum-rank distanceReference 2Reference 1 (Table VI)Singleton-like
42*1192*1122*123
52*1142*1082*122
62*1122*1062*121
72*1072*1002*120
82*106none2*119
92*101none2*118
102*992*882*117
112*96none2*116
122*95none2*115
132*88none2*114
142*872*702*113
152*84none2*112
162*82none2*111
172*77none2*110
182*77none2*109
192*72none2*108
202*71none2*107
212*70none2*106
222*692*522*105
232*67none2*104
242*66none2*103
252*58none2*102
262*58none2*101
272*56none2*100
282*55none2*99
292*51none2*98
302*502*282*97
312*47none2*96
322*46none2*95
382*372*162*89
462*292*82*81
542*202*82*73
#### Table 6： Block length t=127, q=2, n=m=2
Minimum sum-rank distanceReference 2Reference 1 (Table VII)Singleton-like
42*2462*2382*251
52*2402*2332*250
62*2362*2312*249
72*2312*2242*248
102*2212*2102*245
142*2022*1892*241
222*1722*1542*233
302*1462*1122*225
382*1242*862*217
462*1062*702*209
542*912*422*201
622*772*282*193
#### Table 7： Block length t=31, q=3, n=m=2
Minimum sum-rank distanceReference 2Singleton-like
42*572*59
52*532*58
62*522*57
72*492*56
82*472*55
92*442*54
102*422*53
112*402*52
122*392*51
132*362*50
142*352*49
152*322*48
162*312*47
172*292*46
182*282*45
192*252*44
202*242*43
212*222*42
222*212*41
232*202*40
242*192*39
252*182*38
262*172*37
272*152*36
282*142*35
292*132*34
302*132*33
#### Table 8： Block length t=21, q=4, n=m=2
Minimum sum-rank distanceReference 2Singleton-like
42*372*39
52*332*38
62*322*37
72*302*36
82*292*35
92*252*34
102*242*33
#### Table 9： Block length t=12, q=2, n=m=3
Minimum sum-rank distanceReference 2Singleton-like
43*303*33
53*273*32
63*263*31
73*223*30
83*213*29
93*193*28
103*173*27
113*153*26
123*153*25
133*123*24
143*123*23
153*113*22
163*103*21
173*93*20
183*93*19
193*73*18
203*73*17
213*63*16
223*53*15
233*53*14
243*53*13
#### Table 10： Block length t=31, q=2, n=m=3
Minimum sum-rank distanceReference 2Singleton-like
43*893*90
53*833*89
63*823*88
73*773*87
83*753*86
93*723*85
103*703*84
113*673*83
123*663*82
133*613*81
143*593*80
153*563*79
163*543*78
173*523*77
183*513*76
193*483*75
203*473*74
213*443*73
223*413*72
233*403*71
243*393*70