Information on Result #613104
Linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37
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(4162, 4095, F4, 36) (dual of [4095, 3933, 37]-code) | [i] | Truncation | |
| 2 | Linear OA(4181, 4115, F4, 37) (dual of [4115, 3934, 38]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4185, 4120, F4, 37) (dual of [4120, 3935, 38]-code) | [i] | ||
| 4 | Linear OA(4186, 4122, F4, 37) (dual of [4122, 3936, 38]-code) | [i] | ||
| 5 | Linear OA(4188, 4125, F4, 37) (dual of [4125, 3937, 38]-code) | [i] | ||
| 6 | Linear OOA(4163, 2809, F4, 2, 37) (dual of [(2809, 2), 5455, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(4163, 2809, F4, 3, 37) (dual of [(2809, 3), 8264, 38]-NRT-code) | [i] | ||
| 8 | Digital (126, 163, 2809)-net over F4 | [i] | ||
| 9 | Linear OA(4188, 4122, F4, 37) (dual of [4122, 3934, 38]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 10 | Linear OA(4171, 4125, F4, 37) (dual of [4125, 3954, 38]-code) | [i] | Varšamov–Edel Lengthening | |
| 11 | Linear OA(4172, 4141, F4, 37) (dual of [4141, 3969, 38]-code) | [i] | ||
| 12 | Linear OA(4173, 4165, F4, 37) (dual of [4165, 3992, 38]-code) | [i] | ||
| 13 | Linear OA(4174, 4202, F4, 37) (dual of [4202, 4028, 38]-code) | [i] | ||
| 14 | Linear OA(4175, 4256, F4, 37) (dual of [4256, 4081, 38]-code) | [i] | ||
| 15 | Linear OA(4176, 4333, F4, 37) (dual of [4333, 4157, 38]-code) | [i] | ||
| 16 | Linear OA(4177, 4437, F4, 37) (dual of [4437, 4260, 38]-code) | [i] | ||
| 17 | Linear OA(4178, 4569, F4, 37) (dual of [4569, 4391, 38]-code) | [i] | ||
| 18 | Linear OA(4179, 4725, F4, 37) (dual of [4725, 4546, 38]-code) | [i] | ||
| 19 | Linear OA(4180, 4899, F4, 37) (dual of [4899, 4719, 38]-code) | [i] | ||
| 20 | Linear OA(4181, 5086, F4, 37) (dual of [5086, 4905, 38]-code) | [i] | ||
| 21 | Linear OA(4169, 4102, F4, 38) (dual of [4102, 3933, 39]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 22 | Linear OA(4164, 4103, F4, 37) (dual of [4103, 3939, 38]-code) | [i] | ✔ | |
| 23 | Linear OA(4176, 4109, F4, 39) (dual of [4109, 3933, 40]-code) | [i] | ✔ | |
| 24 | Linear OA(4164, 4109, F4, 36) (dual of [4109, 3945, 37]-code) | [i] | ✔ | |
| 25 | Linear OA(4166, 4111, F4, 37) (dual of [4111, 3945, 38]-code) | [i] | ✔ | |
| 26 | Linear OA(4186, 4119, F4, 41) (dual of [4119, 3933, 42]-code) | [i] | ✔ | |
| 27 | Linear OA(4184, 4117, F4, 40) (dual of [4117, 3933, 41]-code) | [i] | ✔ | |
| 28 | Linear OA(4167, 4113, F4, 37) (dual of [4113, 3946, 38]-code) | [i] | ✔ | |
| 29 | Linear OA(4168, 4119, F4, 37) (dual of [4119, 3951, 38]-code) | [i] | ✔ | |
| 30 | Linear OA(4166, 4117, F4, 36) (dual of [4117, 3951, 37]-code) | [i] | ✔ | |
| 31 | Linear OA(4194, 4127, F4, 42) (dual of [4127, 3933, 43]-code) | [i] | ✔ | |
| 32 | Linear OA(4173, 4130, F4, 37) (dual of [4130, 3957, 38]-code) | [i] | ✔ | |
| 33 | Linear OA(4170, 4127, F4, 36) (dual of [4127, 3957, 37]-code) | [i] | ✔ | |
| 34 | Linear OA(4203, 4136, F4, 43) (dual of [4136, 3933, 44]-code) | [i] | ✔ | |
| 35 | Linear OA(4176, 4139, F4, 37) (dual of [4139, 3963, 38]-code) | [i] | ✔ | |
| 36 | Linear OA(4173, 4136, F4, 36) (dual of [4136, 3963, 37]-code) | [i] | ✔ | |
| 37 | Linear OA(4215, 4148, F4, 45) (dual of [4148, 3933, 46]-code) | [i] | ✔ | |
| 38 | Linear OA(4212, 4145, F4, 44) (dual of [4145, 3933, 45]-code) | [i] | ✔ | |
| 39 | Linear OA(4179, 4148, F4, 37) (dual of [4148, 3969, 38]-code) | [i] | ✔ | |
| 40 | Linear OA(4176, 4145, F4, 36) (dual of [4145, 3969, 37]-code) | [i] | ✔ | |
| 41 | Linear OA(4223, 4156, F4, 46) (dual of [4156, 3933, 47]-code) | [i] | ✔ | |
| 42 | Linear OA(4182, 4157, F4, 37) (dual of [4157, 3975, 38]-code) | [i] | ✔ | |
| 43 | Linear OA(4230, 4161, F4, 47) (dual of [4161, 3931, 48]-code) | [i] | ✔ | |
| 44 | Linear OA(4233, 4166, F4, 47) (dual of [4166, 3933, 48]-code) | [i] | ✔ | |
| 45 | Linear OA(4182, 4161, F4, 36) (dual of [4161, 3979, 37]-code) | [i] | ✔ | |
| 46 | Linear OA(4185, 4166, F4, 36) (dual of [4166, 3981, 37]-code) | [i] | ✔ | |
| 47 | Linear OA(4246, 4179, F4, 49) (dual of [4179, 3933, 50]-code) | [i] | ✔ | |
| 48 | Linear OA(4243, 4176, F4, 48) (dual of [4176, 3933, 49]-code) | [i] | ✔ | |
| 49 | Linear OA(4255, 4186, F4, 50) (dual of [4186, 3931, 51]-code) | [i] | ✔ | |
| 50 | Linear OA(4257, 4190, F4, 50) (dual of [4190, 3933, 51]-code) | [i] | ✔ | |
| 51 | Linear OA(4172, 4129, F4, 37) (dual of [4129, 3957, 38]-code) | [i] | ✔ | |
| 52 | Linear OA(4202, 4132, F4, 43) (dual of [4132, 3930, 44]-code) | [i] | ✔ | |
| 53 | Linear OA(4172, 4132, F4, 36) (dual of [4132, 3960, 37]-code) | [i] | ✔ | |
| 54 | Linear OA(4231, 4164, F4, 47) (dual of [4164, 3933, 48]-code) | [i] | ✔ | |
| 55 | Linear OA(4185, 4163, F4, 37) (dual of [4163, 3978, 38]-code) | [i] | ✔ | |
| 56 | Linear OA(4186, 4166, F4, 37) (dual of [4166, 3980, 38]-code) | [i] | ✔ | |
| 57 | Linear OA(4187, 4168, F4, 37) (dual of [4168, 3981, 38]-code) | [i] | ✔ | |
| 58 | Linear OA(4183, 4164, F4, 36) (dual of [4164, 3981, 37]-code) | [i] | ✔ | |
| 59 | Linear OA(4241, 4170, F4, 48) (dual of [4170, 3929, 49]-code) | [i] | ✔ | |
| 60 | Linear OA(4187, 4170, F4, 36) (dual of [4170, 3983, 37]-code) | [i] | ✔ | |
| 61 | Linear OA(4245, 4178, F4, 49) (dual of [4178, 3933, 50]-code) | [i] | ✔ | |
| 62 | Linear OA(4201, 4129, F4, 43) (dual of [4129, 3928, 44]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 63 | Linear OA(4193, 4121, F4, 42) (dual of [4121, 3928, 43]-code) | [i] | ✔ | |
| 64 | Linear OA(4196, 4130, F4, 42) (dual of [4130, 3934, 43]-code) | [i] | ✔ | |
| 65 | Linear OA(4183, 4111, F4, 40) (dual of [4111, 3928, 41]-code) | [i] | ✔ | |
| 66 | Linear OA(4190, 4126, F4, 41) (dual of [4126, 3936, 42]-code) | [i] | ✔ | |
| 67 | Linear OA(4189, 4124, F4, 41) (dual of [4124, 3935, 42]-code) | [i] | ✔ | |
| 68 | Linear OA(4188, 4122, F4, 41) (dual of [4122, 3934, 42]-code) | [i] | ✔ | |
| 69 | Linear OA(4179, 4114, F4, 39) (dual of [4114, 3935, 40]-code) | [i] | ✔ | |
| 70 | Linear OA(4178, 4112, F4, 39) (dual of [4112, 3934, 40]-code) | [i] | ✔ | |
| 71 | Linear OA(4171, 4105, F4, 38) (dual of [4105, 3934, 39]-code) | [i] | ✔ | |
| 72 | Linear OA(4165, 4105, F4, 37) (dual of [4105, 3940, 38]-code) | [i] | ✔ | |
| 73 | Linear OA(4165, 4111, F4, 36) (dual of [4111, 3946, 37]-code) | [i] | ✔ | |
| 74 | Linear OA(4172, 4126, F4, 37) (dual of [4126, 3954, 38]-code) | [i] | ✔ | |
| 75 | Linear OA(4171, 4124, F4, 37) (dual of [4124, 3953, 38]-code) | [i] | ✔ | |
| 76 | Linear OA(4170, 4122, F4, 37) (dual of [4122, 3952, 38]-code) | [i] | ✔ | |
| 77 | Linear OA(4171, 4129, F4, 36) (dual of [4129, 3958, 37]-code) | [i] | ✔ | |
| 78 | Linear OOA(4163, 2048, F4, 2, 37) (dual of [(2048, 2), 3933, 38]-NRT-code) | [i] | OOA Folding | |
| 79 | Linear OOA(4163, 1365, F4, 3, 37) (dual of [(1365, 3), 3932, 38]-NRT-code) | [i] | ||