Information on Result #613279
Linear OA(4196, 1024, F4, 53) (dual of [1024, 828, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4222, 1051, F4, 53) (dual of [1051, 829, 54]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(4201, 1029, F4, 54) (dual of [1029, 828, 55]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 3 | Linear OA(4197, 1030, F4, 53) (dual of [1030, 833, 54]-code) | [i] | ✔ | |
| 4 | Linear OA(4207, 1035, F4, 55) (dual of [1035, 828, 56]-code) | [i] | ✔ | |
| 5 | Linear OA(4197, 1035, F4, 52) (dual of [1035, 838, 53]-code) | [i] | ✔ | |
| 6 | Linear OA(4199, 1037, F4, 53) (dual of [1037, 838, 54]-code) | [i] | ✔ | |
| 7 | Linear OA(4215, 1041, F4, 57) (dual of [1041, 826, 58]-code) | [i] | ✔ | |
| 8 | Linear OA(4216, 1044, F4, 57) (dual of [1044, 828, 58]-code) | [i] | ✔ | |
| 9 | Linear OA(4214, 1042, F4, 56) (dual of [1042, 828, 57]-code) | [i] | ✔ | |
| 10 | Linear OA(4200, 1041, F4, 53) (dual of [1041, 841, 54]-code) | [i] | ✔ | |
| 11 | Linear OA(4201, 1044, F4, 53) (dual of [1044, 843, 54]-code) | [i] | ✔ | |
| 12 | Linear OA(4199, 1042, F4, 52) (dual of [1042, 843, 53]-code) | [i] | ✔ | |
| 13 | Linear OA(4223, 1051, F4, 58) (dual of [1051, 828, 59]-code) | [i] | ✔ | |
| 14 | Linear OA(4206, 1054, F4, 53) (dual of [1054, 848, 54]-code) | [i] | ✔ | |
| 15 | Linear OA(4203, 1051, F4, 52) (dual of [1051, 848, 53]-code) | [i] | ✔ | |
| 16 | Linear OA(4231, 1059, F4, 59) (dual of [1059, 828, 60]-code) | [i] | ✔ | |
| 17 | Linear OA(4208, 1058, F4, 53) (dual of [1058, 850, 54]-code) | [i] | ✔ | |
| 18 | Linear OA(4209, 1062, F4, 53) (dual of [1062, 853, 54]-code) | [i] | ✔ | |
| 19 | Linear OA(4206, 1059, F4, 52) (dual of [1059, 853, 53]-code) | [i] | ✔ | |
| 20 | Linear OA(4241, 1067, F4, 61) (dual of [1067, 826, 62]-code) | [i] | ✔ | |
| 21 | Linear OA(4242, 1070, F4, 61) (dual of [1070, 828, 62]-code) | [i] | ✔ | |
| 22 | Linear OA(4239, 1067, F4, 60) (dual of [1067, 828, 61]-code) | [i] | ✔ | |
| 23 | Linear OA(4211, 1067, F4, 53) (dual of [1067, 856, 54]-code) | [i] | ✔ | |
| 24 | Linear OA(4212, 1070, F4, 53) (dual of [1070, 858, 54]-code) | [i] | ✔ | |
| 25 | Linear OA(4209, 1067, F4, 52) (dual of [1067, 858, 53]-code) | [i] | ✔ | |
| 26 | Linear OA(4249, 1077, F4, 62) (dual of [1077, 828, 63]-code) | [i] | ✔ | |
| 27 | Linear OA(4215, 1078, F4, 53) (dual of [1078, 863, 54]-code) | [i] | ✔ | |
| 28 | Linear OA(4255, 1083, F4, 63) (dual of [1083, 828, 64]-code) | [i] | ✔ | |
| 29 | Linear OA(4218, 1086, F4, 53) (dual of [1086, 868, 54]-code) | [i] | ✔ | |
| 30 | Linear OA(4215, 1083, F4, 52) (dual of [1083, 868, 53]-code) | [i] | ✔ | |
| 31 | Linear OA(4224, 1097, F4, 53) (dual of [1097, 873, 54]-code) | [i] | ✔ | |
| 32 | Linear OA(4218, 1088, F4, 52) (dual of [1088, 870, 53]-code) | [i] | ✔ | |
| 33 | Linear OA(4222, 1095, F4, 52) (dual of [1095, 873, 53]-code) | [i] | ✔ | |
| 34 | Linear OA(4226, 1100, F4, 52) (dual of [1100, 874, 53]-code) | [i] | ✔ | |
| 35 | Linear OA(4221, 1093, F4, 53) (dual of [1093, 872, 54]-code) | [i] | ✔ | |
| 36 | Linear OA(4222, 1095, F4, 53) (dual of [1095, 873, 54]-code) | [i] | ✔ | |
| 37 | Linear OA(4218, 1091, F4, 52) (dual of [1091, 873, 53]-code) | [i] | ✔ | |
| 38 | Linear OA(4230, 1055, F4, 59) (dual of [1055, 825, 60]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 39 | Linear OA(4229, 1053, F4, 59) (dual of [1053, 824, 60]-code) | [i] | ✔ | |
| 40 | Linear OA(4222, 1046, F4, 58) (dual of [1046, 824, 59]-code) | [i] | ✔ | |
| 41 | Linear OA(4228, 1060, F4, 58) (dual of [1060, 832, 59]-code) | [i] | ✔ | |
| 42 | Linear OA(4227, 1058, F4, 58) (dual of [1058, 831, 59]-code) | [i] | ✔ | |
| 43 | Linear OA(4226, 1056, F4, 58) (dual of [1056, 830, 59]-code) | [i] | ✔ | |
| 44 | Linear OA(4225, 1054, F4, 58) (dual of [1054, 829, 59]-code) | [i] | ✔ | |
| 45 | Linear OA(4213, 1037, F4, 56) (dual of [1037, 824, 57]-code) | [i] | ✔ | |
| 46 | Linear OA(4220, 1051, F4, 57) (dual of [1051, 831, 58]-code) | [i] | ✔ | |
| 47 | Linear OA(4219, 1049, F4, 57) (dual of [1049, 830, 58]-code) | [i] | ✔ | |
| 48 | Linear OA(4217, 1047, F4, 56) (dual of [1047, 830, 57]-code) | [i] | ✔ | |
| 49 | Linear OA(4218, 1047, F4, 57) (dual of [1047, 829, 58]-code) | [i] | ✔ | |
| 50 | Linear OA(4216, 1045, F4, 56) (dual of [1045, 829, 57]-code) | [i] | ✔ | |
| 51 | Linear OA(4209, 1038, F4, 55) (dual of [1038, 829, 56]-code) | [i] | ✔ | |
| 52 | Linear OA(4203, 1032, F4, 54) (dual of [1032, 829, 55]-code) | [i] | ✔ | |
| 53 | Linear OA(4198, 1032, F4, 53) (dual of [1032, 834, 54]-code) | [i] | ✔ | |
| 54 | Linear OA(4198, 1037, F4, 52) (dual of [1037, 839, 53]-code) | [i] | ✔ | |
| 55 | Linear OA(4205, 1051, F4, 53) (dual of [1051, 846, 54]-code) | [i] | ✔ | |
| 56 | Linear OA(4204, 1049, F4, 53) (dual of [1049, 845, 54]-code) | [i] | ✔ | |
| 57 | Linear OA(4202, 1047, F4, 52) (dual of [1047, 845, 53]-code) | [i] | ✔ | |
| 58 | Linear OA(4203, 1047, F4, 53) (dual of [1047, 844, 54]-code) | [i] | ✔ | |
| 59 | Linear OA(4201, 1045, F4, 52) (dual of [1045, 844, 53]-code) | [i] | ✔ | |
| 60 | Linear OA(4205, 1055, F4, 52) (dual of [1055, 850, 53]-code) | [i] | ✔ | |
| 61 | Linear OA(4207, 1056, F4, 53) (dual of [1056, 849, 54]-code) | [i] | ✔ | |
| 62 | Linear OA(4204, 1053, F4, 52) (dual of [1053, 849, 53]-code) | [i] | ✔ | |
| 63 | Linear OOA(4196, 512, F4, 2, 53) (dual of [(512, 2), 828, 54]-NRT-code) | [i] | OOA Folding | |