Information on Result #682021
Linear OA(426, 72, F4, 11) (dual of [72, 46, 12]-code), using construction X applied to C([0,5]) ⊂ C([0,4]) based on
- linear OA(425, 65, F4, 11) (dual of [65, 40, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(419, 65, F4, 9) (dual of [65, 46, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(427, 75, F4, 11) (dual of [75, 48, 12]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(4161, 1094, F4, 36) (dual of [1094, 933, 37]-code) | [i] | Construction X with Cyclic Codes | |
| 3 | Linear OA(4162, 1094, F4, 37) (dual of [1094, 932, 38]-code) | [i] | ||
| 4 | Linear OA(4167, 1094, F4, 38) (dual of [1094, 927, 39]-code) | [i] | ||
| 5 | Linear OA(4172, 1094, F4, 39) (dual of [1094, 922, 40]-code) | [i] | ||
| 6 | Linear OA(4176, 1094, F4, 40) (dual of [1094, 918, 41]-code) | [i] | ||
| 7 | Linear OA(4177, 1094, F4, 41) (dual of [1094, 917, 42]-code) | [i] | ||
| 8 | Linear OA(4182, 1094, F4, 42) (dual of [1094, 912, 43]-code) | [i] | ||
| 9 | Linear OA(4191, 1094, F4, 44) (dual of [1094, 903, 45]-code) | [i] | ||
| 10 | Linear OA(4192, 1094, F4, 45) (dual of [1094, 902, 46]-code) | [i] | ||
| 11 | Linear OA(4197, 1094, F4, 46) (dual of [1094, 897, 47]-code) | [i] | ||
| 12 | Linear OA(4202, 1094, F4, 47) (dual of [1094, 892, 48]-code) | [i] | ||
| 13 | Linear OA(4206, 1094, F4, 48) (dual of [1094, 888, 49]-code) | [i] | ||
| 14 | Linear OA(4207, 1094, F4, 49) (dual of [1094, 887, 50]-code) | [i] | ||
| 15 | Linear OA(4212, 1094, F4, 50) (dual of [1094, 882, 51]-code) | [i] | ||
| 16 | Linear OA(4217, 1094, F4, 51) (dual of [1094, 877, 52]-code) | [i] | ||
| 17 | Linear OA(4221, 1094, F4, 52) (dual of [1094, 873, 53]-code) | [i] | ||
| 18 | Linear OA(4222, 1094, F4, 53) (dual of [1094, 872, 54]-code) | [i] | ||
| 19 | Linear OA(4227, 1094, F4, 54) (dual of [1094, 867, 55]-code) | [i] | ||
| 20 | Linear OA(4232, 1094, F4, 55) (dual of [1094, 862, 56]-code) | [i] | ||
| 21 | Linear OA(4236, 1094, F4, 56) (dual of [1094, 858, 57]-code) | [i] | ||
| 22 | Linear OA(4237, 1094, F4, 57) (dual of [1094, 857, 58]-code) | [i] | ||
| 23 | Linear OA(4242, 1094, F4, 58) (dual of [1094, 852, 59]-code) | [i] | ||
| 24 | Linear OA(4247, 1094, F4, 59) (dual of [1094, 847, 60]-code) | [i] | ||
| 25 | Linear OA(4251, 1094, F4, 60) (dual of [1094, 843, 61]-code) | [i] | ||
| 26 | Linear OA(4252, 1094, F4, 61) (dual of [1094, 842, 62]-code) | [i] | ||
| 27 | Linear OA(4257, 1094, F4, 62) (dual of [1094, 837, 63]-code) | [i] | ||
| 28 | Linear OA(4257, 1095, F4, 62) (dual of [1095, 838, 63]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 29 | Linear OA(4252, 1095, F4, 61) (dual of [1095, 843, 62]-code) | [i] | ||
| 30 | Linear OA(4247, 1095, F4, 59) (dual of [1095, 848, 60]-code) | [i] | ||
| 31 | Linear OA(4242, 1095, F4, 58) (dual of [1095, 853, 59]-code) | [i] | ||
| 32 | Linear OA(4237, 1095, F4, 57) (dual of [1095, 858, 58]-code) | [i] | ||
| 33 | Linear OA(4232, 1095, F4, 55) (dual of [1095, 863, 56]-code) | [i] | ||
| 34 | Linear OA(4227, 1095, F4, 54) (dual of [1095, 868, 55]-code) | [i] | ||
| 35 | Linear OA(4222, 1095, F4, 53) (dual of [1095, 873, 54]-code) | [i] | ||
| 36 | Linear OA(4217, 1095, F4, 51) (dual of [1095, 878, 52]-code) | [i] | ||
| 37 | Linear OA(4212, 1095, F4, 50) (dual of [1095, 883, 51]-code) | [i] | ||
| 38 | Linear OA(4207, 1095, F4, 49) (dual of [1095, 888, 50]-code) | [i] | ||
| 39 | Linear OA(4202, 1095, F4, 47) (dual of [1095, 893, 48]-code) | [i] | ||
| 40 | Linear OA(4197, 1095, F4, 46) (dual of [1095, 898, 47]-code) | [i] | ||
| 41 | Linear OA(4192, 1095, F4, 45) (dual of [1095, 903, 46]-code) | [i] | ||
| 42 | Linear OA(4182, 1095, F4, 42) (dual of [1095, 913, 43]-code) | [i] | ||
| 43 | Linear OA(4177, 1095, F4, 41) (dual of [1095, 918, 42]-code) | [i] | ||
| 44 | Linear OA(4172, 1095, F4, 39) (dual of [1095, 923, 40]-code) | [i] | ||
| 45 | Linear OA(4167, 1095, F4, 38) (dual of [1095, 928, 39]-code) | [i] | ||
| 46 | Linear OA(4162, 1095, F4, 37) (dual of [1095, 933, 38]-code) | [i] | ||
| 47 | Linear OOA(426, 36, F4, 2, 11) (dual of [(36, 2), 46, 12]-NRT-code) | [i] | OOA Folding | |