Information on Result #613001

Linear OA(4139, 4096, F4, 31) (dual of [4096, 3957, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31

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(4154, 4112, F4, 31) (dual of [4112, 3958, 32]-code) [i](u, u+v)-Construction
2Linear OA(4157, 4117, F4, 31) (dual of [4117, 3960, 32]-code) [i]
3Linear OA(4158, 4119, F4, 31) (dual of [4119, 3961, 32]-code) [i]
4Linear OA(4160, 4123, F4, 31) (dual of [4123, 3963, 32]-code) [i]
5Linear OOA(4139, 2828, F4, 2, 31) (dual of [(2828, 2), 5517, 32]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
6Linear OOA(4139, 2828, F4, 3, 31) (dual of [(2828, 3), 8345, 32]-NRT-code) [i]
7Digital (108, 139, 2828)-net over F4 [i]
8Linear OA(4160, 4118, F4, 31) (dual of [4118, 3958, 32]-code) [i](u, u−v, u+v+w)-Construction
9Linear OA(4146, 4103, F4, 33) (dual of [4103, 3957, 34]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
10Linear OA(4139, 4102, F4, 31) (dual of [4102, 3963, 32]-code) [i]✔
11Linear OA(4154, 4111, F4, 34) (dual of [4111, 3957, 35]-code) [i]✔
12Linear OA(4140, 4109, F4, 31) (dual of [4109, 3969, 32]-code) [i]✔
13Linear OA(4162, 4119, F4, 35) (dual of [4119, 3957, 36]-code) [i]✔
14Linear OA(4143, 4113, F4, 31) (dual of [4113, 3970, 32]-code) [i]✔
15Linear OA(4144, 4119, F4, 31) (dual of [4119, 3975, 32]-code) [i]✔
16Linear OA(4173, 4130, F4, 37) (dual of [4130, 3957, 38]-code) [i]✔
17Linear OA(4170, 4127, F4, 36) (dual of [4127, 3957, 37]-code) [i]✔
18Linear OA(4146, 4127, F4, 31) (dual of [4127, 3981, 32]-code) [i]✔
19Linear OA(4182, 4139, F4, 38) (dual of [4139, 3957, 39]-code) [i]✔
20Linear OA(4149, 4136, F4, 31) (dual of [4136, 3987, 32]-code) [i]✔
21Linear OA(4191, 4148, F4, 39) (dual of [4148, 3957, 40]-code) [i]✔
22Linear OA(4155, 4148, F4, 31) (dual of [4148, 3993, 32]-code) [i]✔
23Linear OA(4200, 4157, F4, 41) (dual of [4157, 3957, 42]-code) [i]✔
24Linear OA(4157, 4156, F4, 31) (dual of [4156, 3999, 32]-code) [i]✔
25Linear OA(4213, 4170, F4, 42) (dual of [4170, 3957, 43]-code) [i]✔
26Linear OA(4158, 4161, F4, 31) (dual of [4161, 4003, 32]-code) [i]✔
27Linear OA(4222, 4179, F4, 43) (dual of [4179, 3957, 44]-code) [i]✔
28Linear OA(4172, 4129, F4, 37) (dual of [4129, 3957, 38]-code) [i]✔
29Linear OA(4148, 4132, F4, 31) (dual of [4132, 3984, 32]-code) [i]✔
30Linear OA(4209, 4163, F4, 42) (dual of [4163, 3954, 43]-code) [i]✔
31Linear OA(4210, 4166, F4, 42) (dual of [4166, 3956, 43]-code) [i]✔
32Linear OA(4211, 4168, F4, 42) (dual of [4168, 3957, 43]-code) [i]✔
33Linear OA(4159, 4164, F4, 31) (dual of [4164, 4005, 32]-code) [i]✔
34Linear OA(4221, 4178, F4, 43) (dual of [4178, 3957, 44]-code) [i]✔
35Linear OA(4178, 4130, F4, 38) (dual of [4130, 3952, 39]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
36Linear OA(4172, 4126, F4, 37) (dual of [4126, 3954, 38]-code) [i]✔
37Linear OA(4171, 4124, F4, 37) (dual of [4124, 3953, 38]-code) [i]✔
38Linear OA(4170, 4122, F4, 37) (dual of [4122, 3952, 38]-code) [i]✔
39Linear OA(4171, 4129, F4, 36) (dual of [4129, 3958, 37]-code) [i]✔
40Linear OA(4161, 4114, F4, 35) (dual of [4114, 3953, 36]-code) [i]✔
41Linear OA(4163, 4121, F4, 35) (dual of [4121, 3958, 36]-code) [i]✔
42Linear OA(4153, 4105, F4, 34) (dual of [4105, 3952, 35]-code) [i]✔
43Linear OA(4147, 4105, F4, 33) (dual of [4105, 3958, 34]-code) [i]✔
44Linear OA(4143, 4114, F4, 31) (dual of [4114, 3971, 32]-code) [i]✔
45Linear OA(4142, 4112, F4, 31) (dual of [4112, 3970, 32]-code) [i]✔
46Linear OA(4145, 4121, F4, 31) (dual of [4121, 3976, 32]-code) [i]✔
47Linear OA(4147, 4129, F4, 31) (dual of [4129, 3982, 32]-code) [i]✔