Information on Result #700978
Linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,47}, and minimum distance d ≥ |{−1,0,…,5}|+1 = 8 (BCH-bound)
Mode: Constructive and linear.
This result is hidden, because other results with identical parameters exist.
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
- Primitive Cyclic Codes (BCH-Bound) (hidden) [i]
- Primitive Expurgated Narrow-Sense BCH-Codes [i]
- Primitive Cyclic Codes (BCH-Bound) (hidden) [i]
- Primitive Cyclic Codes (BCH-Bound) (hidden) [i]
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(416, 53, F4, 2, 7) (dual of [(53, 2), 90, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(416, 53, F4, 3, 7) (dual of [(53, 3), 143, 8]-NRT-code) | [i] | ||
| 3 | Digital (9, 16, 53)-net over F4 | [i] | ||
| 4 | Linear OA(4255, 16443, F4, 45) (dual of [16443, 16188, 46]-code) | [i] | Construction X with Cyclic Codes | |
| 5 | Linear OA(4241, 16443, F4, 43) (dual of [16443, 16202, 44]-code) | [i] | ||
| 6 | Linear OA(4227, 16443, F4, 41) (dual of [16443, 16216, 42]-code) | [i] | ||
| 7 | Linear OA(4213, 16443, F4, 37) (dual of [16443, 16230, 38]-code) | [i] | ||
| 8 | Linear OA(4199, 16443, F4, 35) (dual of [16443, 16244, 36]-code) | [i] | ||
| 9 | Linear OA(4185, 16443, F4, 33) (dual of [16443, 16258, 34]-code) | [i] | ||
| 10 | Linear OA(4157, 16443, F4, 27) (dual of [16443, 16286, 28]-code) | [i] | ||
| 11 | Linear OA(4143, 16443, F4, 25) (dual of [16443, 16300, 26]-code) | [i] | ||
| 12 | Linear OA(4257, 4149, F4, 53) (dual of [4149, 3892, 54]-code) | [i] | ||
| 13 | Linear OA(4245, 4149, F4, 51) (dual of [4149, 3904, 52]-code) | [i] | ||
| 14 | Linear OA(4233, 4149, F4, 49) (dual of [4149, 3916, 50]-code) | [i] | ||
| 15 | Linear OA(4221, 4149, F4, 45) (dual of [4149, 3928, 46]-code) | [i] | ||
| 16 | Linear OA(4209, 4149, F4, 43) (dual of [4149, 3940, 44]-code) | [i] | ||
| 17 | Linear OA(4197, 4149, F4, 41) (dual of [4149, 3952, 42]-code) | [i] | ||
| 18 | Linear OA(4185, 4149, F4, 37) (dual of [4149, 3964, 38]-code) | [i] | ||
| 19 | Linear OA(4173, 4149, F4, 35) (dual of [4149, 3976, 36]-code) | [i] | ||
| 20 | Linear OA(4161, 4149, F4, 33) (dual of [4149, 3988, 34]-code) | [i] | ||
| 21 | Linear OA(4137, 4149, F4, 27) (dual of [4149, 4012, 28]-code) | [i] | ||
| 22 | Linear OA(4125, 4149, F4, 25) (dual of [4149, 4024, 26]-code) | [i] | ||
| 23 | Linear OA(4257, 1071, F4, 65) (dual of [1071, 814, 66]-code) | [i] | ||
| 24 | Linear OA(4247, 1071, F4, 61) (dual of [1071, 824, 62]-code) | [i] | ||
| 25 | Linear OA(4237, 1071, F4, 59) (dual of [1071, 834, 60]-code) | [i] | ||
| 26 | Linear OA(4227, 1071, F4, 57) (dual of [1071, 844, 58]-code) | [i] | ||
| 27 | Linear OA(4217, 1071, F4, 53) (dual of [1071, 854, 54]-code) | [i] | ||
| 28 | Linear OA(4207, 1071, F4, 51) (dual of [1071, 864, 52]-code) | [i] | ||
| 29 | Linear OA(4197, 1071, F4, 49) (dual of [1071, 874, 50]-code) | [i] | ||
| 30 | Linear OA(4187, 1071, F4, 45) (dual of [1071, 884, 46]-code) | [i] | ||
| 31 | Linear OA(4177, 1071, F4, 43) (dual of [1071, 894, 44]-code) | [i] | ||
| 32 | Linear OA(4167, 1071, F4, 41) (dual of [1071, 904, 42]-code) | [i] | ||
| 33 | Linear OA(4157, 1071, F4, 37) (dual of [1071, 914, 38]-code) | [i] | ||
| 34 | Linear OA(4147, 1071, F4, 35) (dual of [1071, 924, 36]-code) | [i] | ||
| 35 | Linear OA(4137, 1071, F4, 33) (dual of [1071, 934, 34]-code) | [i] | ||
| 36 | Linear OA(4117, 1071, F4, 27) (dual of [1071, 954, 28]-code) | [i] | ||
| 37 | Linear OA(4107, 1071, F4, 25) (dual of [1071, 964, 26]-code) | [i] | ||
| 38 | Linear OA(416, 69, F4, 7) (dual of [69, 53, 8]-code) | [i] | ✔ | Construction XX with Cyclic Codes |
| 39 | Linear OA(419, 69, F4, 8) (dual of [69, 50, 9]-code) | [i] | ✔ | |
| 40 | Linear OA(425, 75, F4, 10) (dual of [75, 50, 11]-code) | [i] | ✔ | |
| 41 | Linear OA(4255, 16442, F4, 46) (dual of [16442, 16187, 47]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 42 | Linear OA(4248, 16442, F4, 45) (dual of [16442, 16194, 46]-code) | [i] | ||
| 43 | Linear OA(4234, 16442, F4, 42) (dual of [16442, 16208, 43]-code) | [i] | ||
| 44 | Linear OA(4220, 16442, F4, 39) (dual of [16442, 16222, 40]-code) | [i] | ||
| 45 | Linear OA(4213, 16442, F4, 38) (dual of [16442, 16229, 39]-code) | [i] | ||
| 46 | Linear OA(4206, 16442, F4, 37) (dual of [16442, 16236, 38]-code) | [i] | ||
| 47 | Linear OA(4192, 16442, F4, 34) (dual of [16442, 16250, 35]-code) | [i] | ||
| 48 | Linear OA(4178, 16442, F4, 31) (dual of [16442, 16264, 32]-code) | [i] | ||
| 49 | Linear OA(4171, 16442, F4, 30) (dual of [16442, 16271, 31]-code) | [i] | ||
| 50 | Linear OA(4164, 16442, F4, 29) (dual of [16442, 16278, 30]-code) | [i] | ||
| 51 | Linear OA(4150, 16442, F4, 26) (dual of [16442, 16292, 27]-code) | [i] | ||
| 52 | Linear OA(4136, 16442, F4, 23) (dual of [16442, 16306, 24]-code) | [i] | ||
| 53 | Linear OA(4257, 4148, F4, 54) (dual of [4148, 3891, 55]-code) | [i] | ||
| 54 | Linear OA(4251, 4148, F4, 53) (dual of [4148, 3897, 54]-code) | [i] | ||
| 55 | Linear OA(4239, 4148, F4, 50) (dual of [4148, 3909, 51]-code) | [i] | ||
| 56 | Linear OA(4227, 4148, F4, 47) (dual of [4148, 3921, 48]-code) | [i] | ||
| 57 | Linear OA(4221, 4148, F4, 46) (dual of [4148, 3927, 47]-code) | [i] | ||
| 58 | Linear OA(4215, 4148, F4, 45) (dual of [4148, 3933, 46]-code) | [i] | ||
| 59 | Linear OA(4203, 4148, F4, 42) (dual of [4148, 3945, 43]-code) | [i] | ||
| 60 | Linear OA(4191, 4148, F4, 39) (dual of [4148, 3957, 40]-code) | [i] | ||
| 61 | Linear OA(4185, 4148, F4, 38) (dual of [4148, 3963, 39]-code) | [i] | ||
| 62 | Linear OA(4179, 4148, F4, 37) (dual of [4148, 3969, 38]-code) | [i] | ||
| 63 | Linear OA(4167, 4148, F4, 34) (dual of [4148, 3981, 35]-code) | [i] | ||
| 64 | Linear OA(4155, 4148, F4, 31) (dual of [4148, 3993, 32]-code) | [i] | ||
| 65 | Linear OA(4149, 4148, F4, 30) (dual of [4148, 3999, 31]-code) | [i] | ||
| 66 | Linear OA(4143, 4148, F4, 29) (dual of [4148, 4005, 30]-code) | [i] | ||
| 67 | Linear OA(4131, 4148, F4, 26) (dual of [4148, 4017, 27]-code) | [i] | ||
| 68 | Linear OA(4252, 1070, F4, 63) (dual of [1070, 818, 64]-code) | [i] | ||
| 69 | Linear OA(4247, 1070, F4, 62) (dual of [1070, 823, 63]-code) | [i] | ||
| 70 | Linear OA(4242, 1070, F4, 61) (dual of [1070, 828, 62]-code) | [i] | ||
| 71 | Linear OA(4232, 1070, F4, 58) (dual of [1070, 838, 59]-code) | [i] | ||
| 72 | Linear OA(4222, 1070, F4, 55) (dual of [1070, 848, 56]-code) | [i] | ||
| 73 | Linear OA(4217, 1070, F4, 54) (dual of [1070, 853, 55]-code) | [i] | ||
| 74 | Linear OA(4212, 1070, F4, 53) (dual of [1070, 858, 54]-code) | [i] | ||
| 75 | Linear OA(4202, 1070, F4, 50) (dual of [1070, 868, 51]-code) | [i] | ||
| 76 | Linear OA(4192, 1070, F4, 47) (dual of [1070, 878, 48]-code) | [i] | ||
| 77 | Linear OA(4187, 1070, F4, 46) (dual of [1070, 883, 47]-code) | [i] | ||
| 78 | Linear OA(4182, 1070, F4, 45) (dual of [1070, 888, 46]-code) | [i] | ||
| 79 | Linear OA(4172, 1070, F4, 42) (dual of [1070, 898, 43]-code) | [i] | ||
| 80 | Linear OA(4162, 1070, F4, 39) (dual of [1070, 908, 40]-code) | [i] | ||
| 81 | Linear OA(4157, 1070, F4, 38) (dual of [1070, 913, 39]-code) | [i] | ||
| 82 | Linear OA(4152, 1070, F4, 37) (dual of [1070, 918, 38]-code) | [i] | ||
| 83 | Linear OA(4142, 1070, F4, 34) (dual of [1070, 928, 35]-code) | [i] | ||
| 84 | Linear OA(4132, 1070, F4, 31) (dual of [1070, 938, 32]-code) | [i] | ||
| 85 | Linear OA(4127, 1070, F4, 30) (dual of [1070, 943, 31]-code) | [i] | ||
| 86 | Linear OA(4122, 1070, F4, 29) (dual of [1070, 948, 30]-code) | [i] | ||
| 87 | Linear OA(4112, 1070, F4, 26) (dual of [1070, 958, 27]-code) | [i] | ||
| 88 | Linear OA(4102, 1070, F4, 23) (dual of [1070, 968, 24]-code) | [i] | ||