Information on Result #613209

Linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45

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(4198, 4095, F4, 44) (dual of [4095, 3897, 45]-code) [i]Truncation
2Linear OA(4221, 4119, F4, 45) (dual of [4119, 3898, 46]-code) [i](u, u+v)-Construction
3Linear OA(4226, 4125, F4, 45) (dual of [4125, 3899, 46]-code) [i]
4Linear OA(4227, 4127, F4, 45) (dual of [4127, 3900, 46]-code) [i]
5Linear OA(4228, 4129, F4, 45) (dual of [4129, 3901, 46]-code) [i]
6Linear OOA(4199, 3298, F4, 2, 45) (dual of [(3298, 2), 6397, 46]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
7Linear OOA(4199, 3298, F4, 3, 45) (dual of [(3298, 3), 9695, 46]-NRT-code) [i]
8Digital (154, 199, 3298)-net over F4 [i]
9Linear OA(4230, 4128, F4, 45) (dual of [4128, 3898, 46]-code) [i](u, u−v, u+v+w)-Construction
10Linear OA(4205, 4122, F4, 45) (dual of [4122, 3917, 46]-code) [i]VarÅ¡amov–Edel Lengthening
11Linear OA(4206, 4141, F4, 45) (dual of [4141, 3935, 46]-code) [i]
12Linear OA(4207, 4172, F4, 45) (dual of [4172, 3965, 46]-code) [i]
13Linear OA(4208, 4219, F4, 45) (dual of [4219, 4011, 46]-code) [i]
14Linear OA(4209, 4285, F4, 45) (dual of [4285, 4076, 46]-code) [i]
15Linear OA(4210, 4373, F4, 45) (dual of [4373, 4163, 46]-code) [i]
16Linear OA(4211, 4483, F4, 45) (dual of [4483, 4272, 46]-code) [i]
17Linear OA(4212, 4611, F4, 45) (dual of [4611, 4399, 46]-code) [i]
18Linear OA(4213, 4750, F4, 45) (dual of [4750, 4537, 46]-code) [i]
19Linear OA(4214, 4899, F4, 45) (dual of [4899, 4685, 46]-code) [i]
20Linear OA(4215, 5054, F4, 45) (dual of [5054, 4839, 46]-code) [i]
21Linear OA(4205, 4102, F4, 46) (dual of [4102, 3897, 47]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
22Linear OA(4200, 4103, F4, 45) (dual of [4103, 3903, 46]-code) [i]✔
23Linear OA(4212, 4109, F4, 47) (dual of [4109, 3897, 48]-code) [i]✔
24Linear OA(4200, 4109, F4, 44) (dual of [4109, 3909, 45]-code) [i]✔
25Linear OA(4202, 4111, F4, 45) (dual of [4111, 3909, 46]-code) [i]✔
26Linear OA(4222, 4119, F4, 49) (dual of [4119, 3897, 50]-code) [i]✔
27Linear OA(4220, 4117, F4, 48) (dual of [4117, 3897, 49]-code) [i]✔
28Linear OA(4203, 4113, F4, 45) (dual of [4113, 3910, 46]-code) [i]✔
29Linear OA(4204, 4119, F4, 45) (dual of [4119, 3915, 46]-code) [i]✔
30Linear OA(4202, 4117, F4, 44) (dual of [4117, 3915, 45]-code) [i]✔
31Linear OA(4230, 4127, F4, 50) (dual of [4127, 3897, 51]-code) [i]✔
32Linear OA(4209, 4130, F4, 45) (dual of [4130, 3921, 46]-code) [i]✔
33Linear OA(4206, 4127, F4, 44) (dual of [4127, 3921, 45]-code) [i]✔
34Linear OA(4239, 4136, F4, 51) (dual of [4136, 3897, 52]-code) [i]✔
35Linear OA(4212, 4139, F4, 45) (dual of [4139, 3927, 46]-code) [i]✔
36Linear OA(4209, 4136, F4, 44) (dual of [4136, 3927, 45]-code) [i]✔
37Linear OA(4251, 4148, F4, 53) (dual of [4148, 3897, 54]-code) [i]✔
38Linear OA(4248, 4145, F4, 52) (dual of [4145, 3897, 53]-code) [i]✔
39Linear OA(4215, 4148, F4, 45) (dual of [4148, 3933, 46]-code) [i]✔
40Linear OA(4212, 4145, F4, 44) (dual of [4145, 3933, 45]-code) [i]✔
41Linear OA(4259, 4156, F4, 54) (dual of [4156, 3897, 55]-code) [i]✔
42Linear OA(4218, 4157, F4, 45) (dual of [4157, 3939, 46]-code) [i]✔
43Linear OA(4225, 4170, F4, 45) (dual of [4170, 3945, 46]-code) [i]✔
44Linear OA(4218, 4161, F4, 44) (dual of [4161, 3943, 45]-code) [i]✔
45Linear OA(4221, 4166, F4, 44) (dual of [4166, 3945, 45]-code) [i]✔
46Linear OA(4228, 4179, F4, 45) (dual of [4179, 3951, 46]-code) [i]✔
47Linear OA(4225, 4176, F4, 44) (dual of [4176, 3951, 45]-code) [i]✔
48Linear OA(4208, 4129, F4, 45) (dual of [4129, 3921, 46]-code) [i]✔
49Linear OA(4238, 4132, F4, 51) (dual of [4132, 3894, 52]-code) [i]✔
50Linear OA(4208, 4132, F4, 44) (dual of [4132, 3924, 45]-code) [i]✔
51Linear OA(4221, 4163, F4, 45) (dual of [4163, 3942, 46]-code) [i]✔
52Linear OA(4222, 4166, F4, 45) (dual of [4166, 3944, 46]-code) [i]✔
53Linear OA(4223, 4168, F4, 45) (dual of [4168, 3945, 46]-code) [i]✔
54Linear OA(4219, 4164, F4, 44) (dual of [4164, 3945, 45]-code) [i]✔
55Linear OA(4223, 4170, F4, 44) (dual of [4170, 3947, 45]-code) [i]✔
56Linear OA(4227, 4178, F4, 45) (dual of [4178, 3951, 46]-code) [i]✔
57Linear OA(4237, 4129, F4, 51) (dual of [4129, 3892, 52]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
58Linear OA(4229, 4121, F4, 50) (dual of [4121, 3892, 51]-code) [i]✔
59Linear OA(4232, 4130, F4, 50) (dual of [4130, 3898, 51]-code) [i]✔
60Linear OA(4219, 4111, F4, 48) (dual of [4111, 3892, 49]-code) [i]✔
61Linear OA(4226, 4126, F4, 49) (dual of [4126, 3900, 50]-code) [i]✔
62Linear OA(4225, 4124, F4, 49) (dual of [4124, 3899, 50]-code) [i]✔
63Linear OA(4224, 4122, F4, 49) (dual of [4122, 3898, 50]-code) [i]✔
64Linear OA(4215, 4114, F4, 47) (dual of [4114, 3899, 48]-code) [i]✔
65Linear OA(4214, 4112, F4, 47) (dual of [4112, 3898, 48]-code) [i]✔
66Linear OA(4207, 4105, F4, 46) (dual of [4105, 3898, 47]-code) [i]✔
67Linear OA(4201, 4105, F4, 45) (dual of [4105, 3904, 46]-code) [i]✔
68Linear OA(4201, 4111, F4, 44) (dual of [4111, 3910, 45]-code) [i]✔
69Linear OA(4208, 4126, F4, 45) (dual of [4126, 3918, 46]-code) [i]✔
70Linear OA(4207, 4124, F4, 45) (dual of [4124, 3917, 46]-code) [i]✔
71Linear OA(4206, 4122, F4, 45) (dual of [4122, 3916, 46]-code) [i]✔
72Linear OA(4207, 4129, F4, 44) (dual of [4129, 3922, 45]-code) [i]✔
73Linear OOA(4199, 2048, F4, 2, 45) (dual of [(2048, 2), 3897, 46]-NRT-code) [i]OOA Folding
74Linear OOA(4199, 1365, F4, 3, 45) (dual of [(1365, 3), 3896, 46]-NRT-code) [i]