Information on Result #612973

Linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29

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:

ResultThis
result
only		Method
1Linear OA(4126, 4095, F4, 28) (dual of [4095, 3969, 29]-code) [i]Truncation
2Linear OA(4141, 4111, F4, 29) (dual of [4111, 3970, 30]-code) [i](u, u+v)-Construction
3Linear OA(4144, 4116, F4, 29) (dual of [4116, 3972, 30]-code) [i]
4Linear OA(4145, 4118, F4, 29) (dual of [4118, 3973, 30]-code) [i]
5Linear OOA(4127, 2328, F4, 2, 29) (dual of [(2328, 2), 4529, 30]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
6Linear OOA(4127, 2328, F4, 3, 29) (dual of [(2328, 3), 6857, 30]-NRT-code) [i]
7Digital (98, 127, 2328)-net over F4 [i]
8Linear OA(4146, 4116, F4, 29) (dual of [4116, 3970, 30]-code) [i](u, u−v, u+v+w)-Construction
9Linear OA(4136, 4134, F4, 29) (dual of [4134, 3998, 30]-code) [i]VarÅ¡amov–Edel Lengthening
10Linear OA(4137, 4154, F4, 29) (dual of [4154, 4017, 30]-code) [i]
11Linear OA(4138, 4183, F4, 29) (dual of [4183, 4045, 30]-code) [i]
12Linear OA(4139, 4225, F4, 29) (dual of [4225, 4086, 30]-code) [i]
13Linear OA(4140, 4285, F4, 29) (dual of [4285, 4145, 30]-code) [i]
14Linear OA(4141, 4367, F4, 29) (dual of [4367, 4226, 30]-code) [i]
15Linear OA(4142, 4476, F4, 29) (dual of [4476, 4334, 30]-code) [i]
16Linear OA(4143, 4616, F4, 29) (dual of [4616, 4473, 30]-code) [i]
17Linear OA(4144, 4788, F4, 29) (dual of [4788, 4644, 30]-code) [i]
18Linear OA(4145, 4992, F4, 29) (dual of [4992, 4847, 30]-code) [i]
19Linear OA(4146, 5223, F4, 29) (dual of [5223, 5077, 30]-code) [i]
20Linear OA(4133, 4102, F4, 30) (dual of [4102, 3969, 31]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
21Linear OA(4128, 4103, F4, 29) (dual of [4103, 3975, 30]-code) [i]✔
22Linear OA(4140, 4109, F4, 31) (dual of [4109, 3969, 32]-code) [i]✔
23Linear OA(4128, 4109, F4, 28) (dual of [4109, 3981, 29]-code) [i]✔
24Linear OA(4130, 4111, F4, 29) (dual of [4111, 3981, 30]-code) [i]✔
25Linear OA(4150, 4119, F4, 33) (dual of [4119, 3969, 34]-code) [i]✔
26Linear OA(4148, 4117, F4, 32) (dual of [4117, 3969, 33]-code) [i]✔
27Linear OA(4131, 4113, F4, 29) (dual of [4113, 3982, 30]-code) [i]✔
28Linear OA(4132, 4119, F4, 29) (dual of [4119, 3987, 30]-code) [i]✔
29Linear OA(4130, 4117, F4, 28) (dual of [4117, 3987, 29]-code) [i]✔
30Linear OA(4158, 4127, F4, 34) (dual of [4127, 3969, 35]-code) [i]✔
31Linear OA(4137, 4130, F4, 29) (dual of [4130, 3993, 30]-code) [i]✔
32Linear OA(4134, 4127, F4, 28) (dual of [4127, 3993, 29]-code) [i]✔
33Linear OA(4167, 4136, F4, 35) (dual of [4136, 3969, 36]-code) [i]✔
34Linear OA(4140, 4139, F4, 29) (dual of [4139, 3999, 30]-code) [i]✔
35Linear OA(4137, 4136, F4, 28) (dual of [4136, 3999, 29]-code) [i]✔
36Linear OA(4179, 4148, F4, 37) (dual of [4148, 3969, 38]-code) [i]✔
37Linear OA(4176, 4145, F4, 36) (dual of [4145, 3969, 37]-code) [i]✔
38Linear OA(4143, 4148, F4, 29) (dual of [4148, 4005, 30]-code) [i]✔
39Linear OA(4140, 4145, F4, 28) (dual of [4145, 4005, 29]-code) [i]✔
40Linear OA(4187, 4156, F4, 38) (dual of [4156, 3969, 39]-code) [i]✔
41Linear OA(4146, 4157, F4, 29) (dual of [4157, 4011, 30]-code) [i]✔
42Linear OA(4194, 4161, F4, 39) (dual of [4161, 3967, 40]-code) [i]✔
43Linear OA(4197, 4166, F4, 39) (dual of [4166, 3969, 40]-code) [i]✔
44Linear OA(4207, 4176, F4, 40) (dual of [4176, 3969, 41]-code) [i]✔
45Linear OA(4136, 4129, F4, 29) (dual of [4129, 3993, 30]-code) [i]✔
46Linear OA(4166, 4132, F4, 35) (dual of [4132, 3966, 36]-code) [i]✔
47Linear OA(4136, 4132, F4, 28) (dual of [4132, 3996, 29]-code) [i]✔
48Linear OA(4195, 4164, F4, 39) (dual of [4164, 3969, 40]-code) [i]✔
49Linear OA(4205, 4170, F4, 40) (dual of [4170, 3965, 41]-code) [i]✔
50Linear OA(4209, 4178, F4, 41) (dual of [4178, 3969, 42]-code) [i]✔
51Linear OA(4165, 4129, F4, 35) (dual of [4129, 3964, 36]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
52Linear OA(4157, 4121, F4, 34) (dual of [4121, 3964, 35]-code) [i]✔
53Linear OA(4160, 4130, F4, 34) (dual of [4130, 3970, 35]-code) [i]✔
54Linear OA(4147, 4111, F4, 32) (dual of [4111, 3964, 33]-code) [i]✔
55Linear OA(4154, 4126, F4, 33) (dual of [4126, 3972, 34]-code) [i]✔
56Linear OA(4153, 4124, F4, 33) (dual of [4124, 3971, 34]-code) [i]✔
57Linear OA(4152, 4122, F4, 33) (dual of [4122, 3970, 34]-code) [i]✔
58Linear OA(4143, 4114, F4, 31) (dual of [4114, 3971, 32]-code) [i]✔
59Linear OA(4142, 4112, F4, 31) (dual of [4112, 3970, 32]-code) [i]✔
60Linear OA(4135, 4105, F4, 30) (dual of [4105, 3970, 31]-code) [i]✔
61Linear OA(4129, 4105, F4, 29) (dual of [4105, 3976, 30]-code) [i]✔
62Linear OA(4129, 4111, F4, 28) (dual of [4111, 3982, 29]-code) [i]✔
63Linear OA(4136, 4126, F4, 29) (dual of [4126, 3990, 30]-code) [i]✔
64Linear OA(4135, 4124, F4, 29) (dual of [4124, 3989, 30]-code) [i]✔
65Linear OA(4134, 4122, F4, 29) (dual of [4122, 3988, 30]-code) [i]✔
66Linear OA(4135, 4129, F4, 28) (dual of [4129, 3994, 29]-code) [i]✔
67Linear OOA(4127, 2048, F4, 2, 29) (dual of [(2048, 2), 3969, 30]-NRT-code) [i]OOA Folding
68Linear OOA(4127, 1365, F4, 3, 29) (dual of [(1365, 3), 3968, 30]-NRT-code) [i]