Information on Result #613281
Linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53
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(4234, 4095, F4, 52) (dual of [4095, 3861, 53]-code) | [i] | Truncation | |
| 2 | Linear OOA(4235, 3789, F4, 2, 53) (dual of [(3789, 2), 7343, 54]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4235, 3789, F4, 3, 53) (dual of [(3789, 3), 11132, 54]-NRT-code) | [i] | ||
| 4 | Digital (182, 235, 3789)-net over F4 | [i] | ||
| 5 | Linear OA(4239, 4132, F4, 53) (dual of [4132, 3893, 54]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(4240, 4171, F4, 53) (dual of [4171, 3931, 54]-code) | [i] | ||
| 7 | Linear OA(4241, 4233, F4, 53) (dual of [4233, 3992, 54]-code) | [i] | ||
| 8 | Linear OA(4242, 4318, F4, 53) (dual of [4318, 4076, 54]-code) | [i] | ||
| 9 | Linear OA(4243, 4421, F4, 53) (dual of [4421, 4178, 54]-code) | [i] | ||
| 10 | Linear OA(4244, 4535, F4, 53) (dual of [4535, 4291, 54]-code) | [i] | ||
| 11 | Linear OA(4245, 4655, F4, 53) (dual of [4655, 4410, 54]-code) | [i] | ||
| 12 | Linear OA(4241, 4102, F4, 54) (dual of [4102, 3861, 55]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 13 | Linear OA(4236, 4103, F4, 53) (dual of [4103, 3867, 54]-code) | [i] | ✔ | |
| 14 | Linear OA(4248, 4109, F4, 55) (dual of [4109, 3861, 56]-code) | [i] | ✔ | |
| 15 | Linear OA(4236, 4109, F4, 52) (dual of [4109, 3873, 53]-code) | [i] | ✔ | |
| 16 | Linear OA(4238, 4111, F4, 53) (dual of [4111, 3873, 54]-code) | [i] | ✔ | |
| 17 | Linear OA(4258, 4119, F4, 57) (dual of [4119, 3861, 58]-code) | [i] | ✔ | |
| 18 | Linear OA(4256, 4117, F4, 56) (dual of [4117, 3861, 57]-code) | [i] | ✔ | |
| 19 | Linear OA(4239, 4113, F4, 53) (dual of [4113, 3874, 54]-code) | [i] | ✔ | |
| 20 | Linear OA(4240, 4119, F4, 53) (dual of [4119, 3879, 54]-code) | [i] | ✔ | |
| 21 | Linear OA(4238, 4117, F4, 52) (dual of [4117, 3879, 53]-code) | [i] | ✔ | |
| 22 | Linear OA(4245, 4130, F4, 53) (dual of [4130, 3885, 54]-code) | [i] | ✔ | |
| 23 | Linear OA(4242, 4127, F4, 52) (dual of [4127, 3885, 53]-code) | [i] | ✔ | |
| 24 | Linear OA(4248, 4139, F4, 53) (dual of [4139, 3891, 54]-code) | [i] | ✔ | |
| 25 | Linear OA(4245, 4136, F4, 52) (dual of [4136, 3891, 53]-code) | [i] | ✔ | |
| 26 | Linear OA(4251, 4148, F4, 53) (dual of [4148, 3897, 54]-code) | [i] | ✔ | |
| 27 | Linear OA(4248, 4145, F4, 52) (dual of [4145, 3897, 53]-code) | [i] | ✔ | |
| 28 | Linear OA(4254, 4157, F4, 53) (dual of [4157, 3903, 54]-code) | [i] | ✔ | |
| 29 | Linear OA(4254, 4161, F4, 52) (dual of [4161, 3907, 53]-code) | [i] | ✔ | |
| 30 | Linear OA(4257, 4166, F4, 52) (dual of [4166, 3909, 53]-code) | [i] | ✔ | |
| 31 | Linear OA(4244, 4129, F4, 53) (dual of [4129, 3885, 54]-code) | [i] | ✔ | |
| 32 | Linear OA(4244, 4132, F4, 52) (dual of [4132, 3888, 53]-code) | [i] | ✔ | |
| 33 | Linear OA(4257, 4163, F4, 53) (dual of [4163, 3906, 54]-code) | [i] | ✔ | |
| 34 | Linear OA(4258, 4166, F4, 53) (dual of [4166, 3908, 54]-code) | [i] | ✔ | |
| 35 | Linear OA(4259, 4168, F4, 53) (dual of [4168, 3909, 54]-code) | [i] | ✔ | |
| 36 | Linear OA(4255, 4164, F4, 52) (dual of [4164, 3909, 53]-code) | [i] | ✔ | |
| 37 | Linear OA(4259, 4170, F4, 52) (dual of [4170, 3911, 53]-code) | [i] | ✔ | |
| 38 | Linear OA(4255, 4111, F4, 56) (dual of [4111, 3856, 57]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 39 | Linear OA(4260, 4122, F4, 57) (dual of [4122, 3862, 58]-code) | [i] | ✔ | |
| 40 | Linear OA(4251, 4114, F4, 55) (dual of [4114, 3863, 56]-code) | [i] | ✔ | |
| 41 | Linear OA(4250, 4112, F4, 55) (dual of [4112, 3862, 56]-code) | [i] | ✔ | |
| 42 | Linear OA(4243, 4105, F4, 54) (dual of [4105, 3862, 55]-code) | [i] | ✔ | |
| 43 | Linear OA(4237, 4105, F4, 53) (dual of [4105, 3868, 54]-code) | [i] | ✔ | |
| 44 | Linear OA(4237, 4111, F4, 52) (dual of [4111, 3874, 53]-code) | [i] | ✔ | |
| 45 | Linear OA(4244, 4126, F4, 53) (dual of [4126, 3882, 54]-code) | [i] | ✔ | |
| 46 | Linear OA(4243, 4124, F4, 53) (dual of [4124, 3881, 54]-code) | [i] | ✔ | |
| 47 | Linear OA(4242, 4122, F4, 53) (dual of [4122, 3880, 54]-code) | [i] | ✔ | |
| 48 | Linear OA(4243, 4129, F4, 52) (dual of [4129, 3886, 53]-code) | [i] | ✔ | |
| 49 | Linear OOA(4235, 2048, F4, 2, 53) (dual of [(2048, 2), 3861, 54]-NRT-code) | [i] | OOA Folding | |
| 50 | Linear OOA(4235, 1365, F4, 3, 53) (dual of [(1365, 3), 3860, 54]-NRT-code) | [i] | ||