Information on Result #613146
Linear OA(4151, 1025, F4, 41) (dual of [1025, 874, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 410−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound)
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(4150, 1024, F4, 40) (dual of [1024, 874, 41]-code) | [i] | Truncation | |
| 2 | Linear OOA(4151, 1025, F4, 2, 41) (dual of [(1025, 2), 1899, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4151, 1025, F4, 3, 41) (dual of [(1025, 3), 2924, 42]-NRT-code) | [i] | ||
| 4 | Digital (110, 151, 1025)-net over F4 | [i] | ||
| 5 | Linear OA(4152, 1047, F4, 41) (dual of [1047, 895, 42]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(4153, 1078, F4, 41) (dual of [1078, 925, 42]-code) | [i] | ||
| 7 | Linear OA(4170, 1045, F4, 41) (dual of [1045, 875, 42]-code) | [i] | ✔ | Construction X with Cyclic Codes |
| 8 | Linear OA(4162, 1036, F4, 43) (dual of [1036, 874, 44]-code) | [i] | ✔ | |
| 9 | Linear OA(4152, 1036, F4, 39) (dual of [1036, 884, 40]-code) | [i] | ✔ | |
| 10 | Linear OA(4154, 1031, F4, 41) (dual of [1031, 877, 42]-code) | [i] | ✔ | |
| 11 | Linear OA(4155, 1039, F4, 41) (dual of [1039, 884, 42]-code) | [i] | ✔ | |
| 12 | Linear OA(4175, 1042, F4, 45) (dual of [1042, 867, 46]-code) | [i] | ✔ | |
| 13 | Linear OA(4176, 1050, F4, 45) (dual of [1050, 874, 46]-code) | [i] | ✔ | |
| 14 | Linear OA(4174, 1046, F4, 44) (dual of [1046, 872, 45]-code) | [i] | ✔ | |
| 15 | Linear OA(4160, 1049, F4, 41) (dual of [1049, 889, 42]-code) | [i] | ✔ | |
| 16 | Linear OA(4161, 1055, F4, 41) (dual of [1055, 894, 42]-code) | [i] | ✔ | |
| 17 | Linear OA(4157, 1046, F4, 40) (dual of [1046, 889, 41]-code) | [i] | ✔ | |
| 18 | Linear OA(4158, 1052, F4, 40) (dual of [1052, 894, 41]-code) | [i] | ✔ | |
| 19 | Linear OA(4155, 1042, F4, 39) (dual of [1042, 887, 40]-code) | [i] | ✔ | |
| 20 | Linear OA(4156, 1050, F4, 39) (dual of [1050, 894, 40]-code) | [i] | ✔ | |
| 21 | Linear OA(4154, 1046, F4, 38) (dual of [1046, 892, 39]-code) | [i] | ✔ | |
| 22 | Linear OA(4194, 1059, F4, 49) (dual of [1059, 865, 50]-code) | [i] | ✔ | |
| 23 | Linear OA(4195, 1062, F4, 49) (dual of [1062, 867, 50]-code) | [i] | ✔ | |
| 24 | Linear OA(4196, 1068, F4, 49) (dual of [1068, 872, 50]-code) | [i] | ✔ | |
| 25 | Linear OA(4197, 1071, F4, 49) (dual of [1071, 874, 50]-code) | [i] | ✔ | |
| 26 | Linear OA(4193, 1059, F4, 48) (dual of [1059, 866, 49]-code) | [i] | ✔ | |
| 27 | Linear OA(4194, 1068, F4, 48) (dual of [1068, 874, 49]-code) | [i] | ✔ | |
| 28 | Linear OA(4191, 1065, F4, 47) (dual of [1065, 874, 48]-code) | [i] | ✔ | |
| 29 | Linear OA(4188, 1062, F4, 46) (dual of [1062, 874, 47]-code) | [i] | ✔ | |
| 30 | Linear OA(4164, 1059, F4, 41) (dual of [1059, 895, 42]-code) | [i] | ✔ | |
| 31 | Linear OA(4165, 1062, F4, 41) (dual of [1062, 897, 42]-code) | [i] | ✔ | |
| 32 | Linear OA(4166, 1068, F4, 41) (dual of [1068, 902, 42]-code) | [i] | ✔ | |
| 33 | Linear OA(4167, 1071, F4, 41) (dual of [1071, 904, 42]-code) | [i] | ✔ | |
| 34 | Linear OA(4163, 1059, F4, 40) (dual of [1059, 896, 41]-code) | [i] | ✔ | |
| 35 | Linear OA(4164, 1068, F4, 40) (dual of [1068, 904, 41]-code) | [i] | ✔ | |
| 36 | Linear OA(4161, 1065, F4, 39) (dual of [1065, 904, 40]-code) | [i] | ✔ | |
| 37 | Linear OA(4158, 1062, F4, 38) (dual of [1062, 904, 39]-code) | [i] | ✔ | |
| 38 | Linear OA(4210, 1084, F4, 51) (dual of [1084, 874, 52]-code) | [i] | ✔ | |
| 39 | Linear OA(4176, 1090, F4, 41) (dual of [1090, 914, 42]-code) | [i] | ✔ | |
| 40 | Linear OA(4173, 1087, F4, 40) (dual of [1087, 914, 41]-code) | [i] | ✔ | |
| 41 | Linear OA(4170, 1084, F4, 39) (dual of [1084, 914, 40]-code) | [i] | ✔ | |
| 42 | Linear OA(4223, 1089, F4, 52) (dual of [1089, 866, 53]-code) | [i] | ✔ | |
| 43 | Linear OA(4227, 1101, F4, 52) (dual of [1101, 874, 53]-code) | [i] | ✔ | |
| 44 | Linear OA(4225, 1099, F4, 52) (dual of [1099, 874, 53]-code) | [i] | ✔ | |
| 45 | Linear OA(4193, 1061, F4, 48) (dual of [1061, 868, 49]-code) | [i] | ✔ | Construction XX with a Chain of Cyclic Codes |
| 46 | Linear OA(4192, 1059, F4, 48) (dual of [1059, 867, 49]-code) | [i] | ✔ | |
| 47 | Linear OA(4190, 1057, F4, 47) (dual of [1057, 867, 48]-code) | [i] | ✔ | |
| 48 | Linear OA(4185, 1064, F4, 45) (dual of [1064, 879, 46]-code) | [i] | ✔ | |
| 49 | Linear OA(4184, 1062, F4, 45) (dual of [1062, 878, 46]-code) | [i] | ✔ | |
| 50 | Linear OA(4182, 1059, F4, 45) (dual of [1059, 877, 46]-code) | [i] | ✔ | |
| 51 | Linear OA(4168, 1045, F4, 43) (dual of [1045, 877, 44]-code) | [i] | ✔ | |
| 52 | Linear OA(4159, 1046, F4, 41) (dual of [1046, 887, 42]-code) | [i] | ✔ | |
| 53 | Linear OA(4163, 1061, F4, 40) (dual of [1061, 898, 41]-code) | [i] | ✔ | |
| 54 | Linear OA(4162, 1059, F4, 40) (dual of [1059, 897, 41]-code) | [i] | ✔ | |
| 55 | Linear OA(4160, 1057, F4, 39) (dual of [1057, 897, 40]-code) | [i] | ✔ | |