Information on Result #613314
Linear OA(4211, 1025, F4, 57) (dual of [1025, 814, 58]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 410−1, defining interval I = [0,28], and minimum distance d ≥ |{−28,−27,…,28}|+1 = 58 (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(4210, 1024, F4, 56) (dual of [1024, 814, 57]-code) | [i] | Truncation | |
| 2 | Linear OA(4238, 1053, F4, 57) (dual of [1053, 815, 58]-code) | [i] | ✔ | Construction X with Cyclic Codes |
| 3 | Linear OA(4222, 1036, F4, 59) (dual of [1036, 814, 60]-code) | [i] | ✔ | |
| 4 | Linear OA(4212, 1036, F4, 55) (dual of [1036, 824, 56]-code) | [i] | ✔ | |
| 5 | Linear OA(4214, 1031, F4, 57) (dual of [1031, 817, 58]-code) | [i] | ✔ | |
| 6 | Linear OA(4215, 1039, F4, 57) (dual of [1039, 824, 58]-code) | [i] | ✔ | |
| 7 | Linear OA(4235, 1042, F4, 61) (dual of [1042, 807, 62]-code) | [i] | ✔ | |
| 8 | Linear OA(4236, 1050, F4, 61) (dual of [1050, 814, 62]-code) | [i] | ✔ | |
| 9 | Linear OA(4234, 1046, F4, 60) (dual of [1046, 812, 61]-code) | [i] | ✔ | |
| 10 | Linear OA(4220, 1049, F4, 57) (dual of [1049, 829, 58]-code) | [i] | ✔ | |
| 11 | Linear OA(4221, 1055, F4, 57) (dual of [1055, 834, 58]-code) | [i] | ✔ | |
| 12 | Linear OA(4217, 1046, F4, 56) (dual of [1046, 829, 57]-code) | [i] | ✔ | |
| 13 | Linear OA(4218, 1052, F4, 56) (dual of [1052, 834, 57]-code) | [i] | ✔ | |
| 14 | Linear OA(4215, 1042, F4, 55) (dual of [1042, 827, 56]-code) | [i] | ✔ | |
| 15 | Linear OA(4216, 1050, F4, 55) (dual of [1050, 834, 56]-code) | [i] | ✔ | |
| 16 | Linear OA(4214, 1046, F4, 54) (dual of [1046, 832, 55]-code) | [i] | ✔ | |
| 17 | Linear OA(4254, 1059, F4, 65) (dual of [1059, 805, 66]-code) | [i] | ✔ | |
| 18 | Linear OA(4255, 1062, F4, 65) (dual of [1062, 807, 66]-code) | [i] | ✔ | |
| 19 | Linear OA(4256, 1068, F4, 65) (dual of [1068, 812, 66]-code) | [i] | ✔ | |
| 20 | Linear OA(4257, 1071, F4, 65) (dual of [1071, 814, 66]-code) | [i] | ✔ | |
| 21 | Linear OA(4253, 1059, F4, 64) (dual of [1059, 806, 65]-code) | [i] | ✔ | |
| 22 | Linear OA(4254, 1068, F4, 64) (dual of [1068, 814, 65]-code) | [i] | ✔ | |
| 23 | Linear OA(4251, 1065, F4, 63) (dual of [1065, 814, 64]-code) | [i] | ✔ | |
| 24 | Linear OA(4248, 1062, F4, 62) (dual of [1062, 814, 63]-code) | [i] | ✔ | |
| 25 | Linear OA(4224, 1059, F4, 57) (dual of [1059, 835, 58]-code) | [i] | ✔ | |
| 26 | Linear OA(4225, 1062, F4, 57) (dual of [1062, 837, 58]-code) | [i] | ✔ | |
| 27 | Linear OA(4226, 1068, F4, 57) (dual of [1068, 842, 58]-code) | [i] | ✔ | |
| 28 | Linear OA(4227, 1071, F4, 57) (dual of [1071, 844, 58]-code) | [i] | ✔ | |
| 29 | Linear OA(4223, 1059, F4, 56) (dual of [1059, 836, 57]-code) | [i] | ✔ | |
| 30 | Linear OA(4224, 1068, F4, 56) (dual of [1068, 844, 57]-code) | [i] | ✔ | |
| 31 | Linear OA(4221, 1065, F4, 55) (dual of [1065, 844, 56]-code) | [i] | ✔ | |
| 32 | Linear OA(4218, 1062, F4, 54) (dual of [1062, 844, 55]-code) | [i] | ✔ | |
| 33 | Linear OA(4236, 1090, F4, 57) (dual of [1090, 854, 58]-code) | [i] | ✔ | |
| 34 | Linear OA(4233, 1087, F4, 56) (dual of [1087, 854, 57]-code) | [i] | ✔ | |
| 35 | Linear OA(4230, 1084, F4, 55) (dual of [1084, 854, 56]-code) | [i] | ✔ | |
| 36 | Linear OA(4243, 1101, F4, 57) (dual of [1101, 858, 58]-code) | [i] | ✔ | |
| 37 | Linear OA(4244, 1108, F4, 57) (dual of [1108, 864, 58]-code) | [i] | ✔ | |
| 38 | Linear OA(4241, 1101, F4, 56) (dual of [1101, 860, 57]-code) | [i] | ✔ | |
| 39 | Linear OA(4239, 1101, F4, 55) (dual of [1101, 862, 56]-code) | [i] | ✔ | |
| 40 | Linear OA(4240, 1104, F4, 55) (dual of [1104, 864, 56]-code) | [i] | ✔ | |
| 41 | Linear OA(4233, 1089, F4, 54) (dual of [1089, 856, 55]-code) | [i] | ✔ | |
| 42 | Linear OA(4243, 1102, F4, 57) (dual of [1102, 859, 58]-code) | [i] | ✔ | |
| 43 | Linear OA(4253, 1061, F4, 64) (dual of [1061, 808, 65]-code) | [i] | ✔ | Construction XX with a Chain of Cyclic Codes |
| 44 | Linear OA(4252, 1059, F4, 64) (dual of [1059, 807, 65]-code) | [i] | ✔ | |
| 45 | Linear OA(4250, 1057, F4, 63) (dual of [1057, 807, 64]-code) | [i] | ✔ | |
| 46 | Linear OA(4245, 1064, F4, 61) (dual of [1064, 819, 62]-code) | [i] | ✔ | |
| 47 | Linear OA(4244, 1062, F4, 61) (dual of [1062, 818, 62]-code) | [i] | ✔ | |
| 48 | Linear OA(4242, 1059, F4, 61) (dual of [1059, 817, 62]-code) | [i] | ✔ | |
| 49 | Linear OA(4228, 1045, F4, 59) (dual of [1045, 817, 60]-code) | [i] | ✔ | |
| 50 | Linear OA(4219, 1046, F4, 57) (dual of [1046, 827, 58]-code) | [i] | ✔ | |
| 51 | Linear OA(4223, 1061, F4, 56) (dual of [1061, 838, 57]-code) | [i] | ✔ | |
| 52 | Linear OA(4222, 1059, F4, 56) (dual of [1059, 837, 57]-code) | [i] | ✔ | |
| 53 | Linear OA(4220, 1057, F4, 55) (dual of [1057, 837, 56]-code) | [i] | ✔ | |