Information on Result #615210
Linear OA(8141, 4096, F8, 41) (dual of [4096, 3955, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41
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(8140, 4095, F8, 40) (dual of [4095, 3955, 41]-code) | [i] | Truncation | |
| 2 | Linear OA(8161, 4117, F8, 41) (dual of [4117, 3956, 42]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OOA(8141, 3815, F8, 2, 41) (dual of [(3815, 2), 7489, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(8141, 3815, F8, 3, 41) (dual of [(3815, 3), 11304, 42]-NRT-code) | [i] | ||
| 5 | Digital (100, 141, 3815)-net over F8 | [i] | ||
| 6 | Linear OA(8144, 4150, F8, 41) (dual of [4150, 4006, 42]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(8145, 4281, F8, 41) (dual of [4281, 4136, 42]-code) | [i] | ||
| 8 | Linear OA(8146, 4482, F8, 41) (dual of [4482, 4336, 42]-code) | [i] | ||
| 9 | Linear OA(8147, 4715, F8, 41) (dual of [4715, 4568, 42]-code) | [i] | ||
| 10 | Linear OA(8148, 4965, F8, 41) (dual of [4965, 4817, 42]-code) | [i] | ||
| 11 | Linear OA(8145, 4100, F8, 42) (dual of [4100, 3955, 43]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 12 | Linear OA(8142, 4101, F8, 41) (dual of [4101, 3959, 42]-code) | [i] | ✔ | |
| 13 | Linear OA(8150, 4105, F8, 43) (dual of [4105, 3955, 44]-code) | [i] | ✔ | |
| 14 | Linear OA(8142, 4105, F8, 40) (dual of [4105, 3963, 41]-code) | [i] | ✔ | |
| 15 | Linear OA(8143, 4105, F8, 41) (dual of [4105, 3962, 42]-code) | [i] | ✔ | |
| 16 | Linear OA(8144, 4107, F8, 41) (dual of [4107, 3963, 42]-code) | [i] | ✔ | |
| 17 | Linear OA(8156, 4111, F8, 44) (dual of [4111, 3955, 45]-code) | [i] | ✔ | |
| 18 | Linear OA(8145, 4112, F8, 41) (dual of [4112, 3967, 42]-code) | [i] | ✔ | |
| 19 | Linear OA(8161, 4116, F8, 45) (dual of [4116, 3955, 46]-code) | [i] | ✔ | |
| 20 | Linear OA(8147, 4118, F8, 41) (dual of [4118, 3971, 42]-code) | [i] | ✔ | |
| 21 | Linear OA(8145, 4116, F8, 40) (dual of [4116, 3971, 41]-code) | [i] | ✔ | |
| 22 | Linear OA(8167, 4122, F8, 46) (dual of [4122, 3955, 47]-code) | [i] | ✔ | |
| 23 | Linear OA(8148, 4123, F8, 41) (dual of [4123, 3975, 42]-code) | [i] | ✔ | |
| 24 | Linear OA(8172, 4127, F8, 47) (dual of [4127, 3955, 48]-code) | [i] | ✔ | |
| 25 | Linear OA(8152, 4131, F8, 41) (dual of [4131, 3979, 42]-code) | [i] | ✔ | |
| 26 | Linear OA(8148, 4127, F8, 40) (dual of [4127, 3979, 41]-code) | [i] | ✔ | |
| 27 | Linear OA(8154, 4137, F8, 41) (dual of [4137, 3983, 42]-code) | [i] | ✔ | |
| 28 | Linear OA(8152, 4135, F8, 40) (dual of [4135, 3983, 41]-code) | [i] | ✔ | |
| 29 | Linear OA(8156, 4143, F8, 41) (dual of [4143, 3987, 42]-code) | [i] | ✔ | |
| 30 | Linear OA(8157, 4148, F8, 41) (dual of [4148, 3991, 42]-code) | [i] | ✔ | |
| 31 | Linear OA(8159, 4154, F8, 41) (dual of [4154, 3995, 42]-code) | [i] | ✔ | |
| 32 | Linear OA(8157, 4152, F8, 40) (dual of [4152, 3995, 41]-code) | [i] | ✔ | |
| 33 | Linear OA(8161, 4160, F8, 41) (dual of [4160, 3999, 42]-code) | [i] | ✔ | |
| 34 | Linear OA(8146, 4116, F8, 41) (dual of [4116, 3970, 42]-code) | [i] | ✔ | |
| 35 | Linear OA(8151, 4130, F8, 41) (dual of [4130, 3979, 42]-code) | [i] | ✔ | |
| 36 | Linear OA(8151, 4134, F8, 40) (dual of [4134, 3983, 41]-code) | [i] | ✔ | |
| 37 | Linear OA(8166, 4118, F8, 46) (dual of [4118, 3952, 47]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 38 | Linear OA(8171, 4129, F8, 46) (dual of [4129, 3958, 47]-code) | [i] | ✔ | |
| 39 | Linear OA(8170, 4127, F8, 46) (dual of [4127, 3957, 47]-code) | [i] | ✔ | |
| 40 | Linear OA(8169, 4125, F8, 46) (dual of [4125, 3956, 47]-code) | [i] | ✔ | |
| 41 | Linear OA(8163, 4119, F8, 45) (dual of [4119, 3956, 46]-code) | [i] | ✔ | |
| 42 | Linear OA(8155, 4107, F8, 44) (dual of [4107, 3952, 45]-code) | [i] | ✔ | |
| 43 | Linear OA(8158, 4114, F8, 44) (dual of [4114, 3956, 45]-code) | [i] | ✔ | |
| 44 | Linear OA(8152, 4108, F8, 43) (dual of [4108, 3956, 44]-code) | [i] | ✔ | |
| 45 | Linear OA(8143, 4107, F8, 40) (dual of [4107, 3964, 41]-code) | [i] | ✔ | |
| 46 | Linear OA(8146, 4114, F8, 41) (dual of [4114, 3968, 42]-code) | [i] | ✔ | |
| 47 | Linear OA(8146, 4118, F8, 40) (dual of [4118, 3972, 41]-code) | [i] | ✔ | |
| 48 | Linear OA(8151, 4129, F8, 41) (dual of [4129, 3978, 42]-code) | [i] | ✔ | |
| 49 | Linear OA(8150, 4127, F8, 41) (dual of [4127, 3977, 42]-code) | [i] | ✔ | |
| 50 | Linear OA(8149, 4125, F8, 41) (dual of [4125, 3976, 42]-code) | [i] | ✔ | |
| 51 | Linear OOA(8141, 2048, F8, 2, 41) (dual of [(2048, 2), 3955, 42]-NRT-code) | [i] | OOA Folding | |
| 52 | Linear OOA(8141, 1365, F8, 3, 41) (dual of [(1365, 3), 3954, 42]-NRT-code) | [i] | ||