Information on Result #679577

Linear OA(4181, 4096, F4, 41) (dual of [4096, 3915, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41

Mode: Constructive and linear.

This result is hidden, because other results with identical parameters exist.

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:

ResultThis
result
only		Method
1Linear OOA(4181, 3053, F4, 2, 41) (dual of [(3053, 2), 5925, 42]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4181, 3053, F4, 3, 41) (dual of [(3053, 3), 8978, 42]-NRT-code) [i]
3Digital (140, 181, 3053)-net over F4 [i]
4Linear OA(4187, 4102, F4, 42) (dual of [4102, 3915, 43]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
5Linear OA(4182, 4103, F4, 41) (dual of [4103, 3921, 42]-code) [i]✔
6Linear OA(4182, 4109, F4, 40) (dual of [4109, 3927, 41]-code) [i]✔
7Linear OA(4184, 4111, F4, 41) (dual of [4111, 3927, 42]-code) [i]✔
8Linear OA(4203, 4113, F4, 45) (dual of [4113, 3910, 46]-code) [i]✔
9Linear OA(4204, 4119, F4, 45) (dual of [4119, 3915, 46]-code) [i]✔
10Linear OA(4202, 4117, F4, 44) (dual of [4117, 3915, 45]-code) [i]✔
11Linear OA(4186, 4119, F4, 41) (dual of [4119, 3933, 42]-code) [i]✔
12Linear OA(4184, 4117, F4, 40) (dual of [4117, 3933, 41]-code) [i]✔
13Linear OA(4212, 4127, F4, 46) (dual of [4127, 3915, 47]-code) [i]✔
14Linear OA(4221, 4136, F4, 47) (dual of [4136, 3915, 48]-code) [i]✔
15Linear OA(4194, 4139, F4, 41) (dual of [4139, 3945, 42]-code) [i]✔
16Linear OA(4191, 4136, F4, 40) (dual of [4136, 3945, 41]-code) [i]✔
17Linear OA(4241, 4156, F4, 50) (dual of [4156, 3915, 51]-code) [i]✔
18Linear OA(4200, 4157, F4, 41) (dual of [4157, 3957, 42]-code) [i]✔
19Linear OA(4207, 4170, F4, 41) (dual of [4170, 3963, 42]-code) [i]✔
20Linear OA(4200, 4161, F4, 40) (dual of [4161, 3961, 41]-code) [i]✔
21Linear OA(4203, 4166, F4, 40) (dual of [4166, 3963, 41]-code) [i]✔
22Linear OA(4207, 4176, F4, 40) (dual of [4176, 3969, 41]-code) [i]✔
23Linear OA(4220, 4132, F4, 47) (dual of [4132, 3912, 48]-code) [i]✔
24Linear OA(4190, 4132, F4, 40) (dual of [4132, 3942, 41]-code) [i]✔
25Linear OA(4203, 4163, F4, 41) (dual of [4163, 3960, 42]-code) [i]✔
26Linear OA(4204, 4166, F4, 41) (dual of [4166, 3962, 42]-code) [i]✔
27Linear OA(4205, 4168, F4, 41) (dual of [4168, 3963, 42]-code) [i]✔
28Linear OA(4201, 4164, F4, 40) (dual of [4164, 3963, 41]-code) [i]✔
29Linear OA(4259, 4170, F4, 52) (dual of [4170, 3911, 53]-code) [i]✔
30Linear OA(4205, 4170, F4, 40) (dual of [4170, 3965, 41]-code) [i]✔
31Linear OA(4209, 4178, F4, 41) (dual of [4178, 3969, 42]-code) [i]✔
32Linear OA(4219, 4129, F4, 47) (dual of [4129, 3910, 48]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
33Linear OA(4211, 4121, F4, 46) (dual of [4121, 3910, 47]-code) [i]✔
34Linear OA(4214, 4130, F4, 46) (dual of [4130, 3916, 47]-code) [i]✔
35Linear OA(4201, 4111, F4, 44) (dual of [4111, 3910, 45]-code) [i]✔
36Linear OA(4208, 4126, F4, 45) (dual of [4126, 3918, 46]-code) [i]✔
37Linear OA(4207, 4124, F4, 45) (dual of [4124, 3917, 46]-code) [i]✔
38Linear OA(4206, 4122, F4, 45) (dual of [4122, 3916, 46]-code) [i]✔
39Linear OA(4197, 4114, F4, 43) (dual of [4114, 3917, 44]-code) [i]✔
40Linear OA(4189, 4105, F4, 42) (dual of [4105, 3916, 43]-code) [i]✔
41Linear OA(4183, 4105, F4, 41) (dual of [4105, 3922, 42]-code) [i]✔
42Linear OA(4183, 4111, F4, 40) (dual of [4111, 3928, 41]-code) [i]✔
43Linear OA(4190, 4126, F4, 41) (dual of [4126, 3936, 42]-code) [i]✔
44Linear OA(4189, 4124, F4, 41) (dual of [4124, 3935, 42]-code) [i]✔
45Linear OA(4188, 4122, F4, 41) (dual of [4122, 3934, 42]-code) [i]✔
46Linear OOA(4181, 2048, F4, 2, 41) (dual of [(2048, 2), 3915, 42]-NRT-code) [i]OOA Folding
47Linear OOA(4181, 1365, F4, 3, 41) (dual of [(1365, 3), 3914, 42]-NRT-code) [i]