Information on Result #613127

Linear OA(4175, 4096, F4, 39) (dual of [4096, 3921, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39

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(4194, 4116, F4, 39) (dual of [4116, 3922, 40]-code) [i](u, u+v)-Construction
2Linear OA(4198, 4121, F4, 39) (dual of [4121, 3923, 40]-code) [i]
3Linear OA(4199, 4123, F4, 39) (dual of [4123, 3924, 40]-code) [i]
4Linear OA(4201, 4126, F4, 39) (dual of [4126, 3925, 40]-code) [i]
5Linear OOA(4175, 3283, F4, 2, 39) (dual of [(3283, 2), 6391, 40]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
6Linear OOA(4175, 3283, F4, 3, 39) (dual of [(3283, 3), 9674, 40]-NRT-code) [i]
7Digital (136, 175, 3283)-net over F4 [i]
8Linear OA(4202, 4124, F4, 39) (dual of [4124, 3922, 40]-code) [i](u, u−v, u+v+w)-Construction
9Linear OA(4182, 4103, F4, 41) (dual of [4103, 3921, 42]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
10Linear OA(4175, 4102, F4, 39) (dual of [4102, 3927, 40]-code) [i]✔
11Linear OA(4190, 4111, F4, 42) (dual of [4111, 3921, 43]-code) [i]✔
12Linear OA(4176, 4109, F4, 39) (dual of [4109, 3933, 40]-code) [i]✔
13Linear OA(4198, 4119, F4, 43) (dual of [4119, 3921, 44]-code) [i]✔
14Linear OA(4179, 4113, F4, 39) (dual of [4113, 3934, 40]-code) [i]✔
15Linear OA(4180, 4119, F4, 39) (dual of [4119, 3939, 40]-code) [i]✔
16Linear OA(4209, 4130, F4, 45) (dual of [4130, 3921, 46]-code) [i]✔
17Linear OA(4206, 4127, F4, 44) (dual of [4127, 3921, 45]-code) [i]✔
18Linear OA(4182, 4127, F4, 39) (dual of [4127, 3945, 40]-code) [i]✔
19Linear OA(4218, 4139, F4, 46) (dual of [4139, 3921, 47]-code) [i]✔
20Linear OA(4185, 4136, F4, 39) (dual of [4136, 3951, 40]-code) [i]✔
21Linear OA(4227, 4148, F4, 47) (dual of [4148, 3921, 48]-code) [i]✔
22Linear OA(4191, 4148, F4, 39) (dual of [4148, 3957, 40]-code) [i]✔
23Linear OA(4236, 4157, F4, 49) (dual of [4157, 3921, 50]-code) [i]✔
24Linear OA(4193, 4156, F4, 39) (dual of [4156, 3963, 40]-code) [i]✔
25Linear OA(4249, 4170, F4, 50) (dual of [4170, 3921, 51]-code) [i]✔
26Linear OA(4194, 4161, F4, 39) (dual of [4161, 3967, 40]-code) [i]✔
27Linear OA(4197, 4166, F4, 39) (dual of [4166, 3969, 40]-code) [i]✔
28Linear OA(4258, 4179, F4, 51) (dual of [4179, 3921, 52]-code) [i]✔
29Linear OA(4208, 4129, F4, 45) (dual of [4129, 3921, 46]-code) [i]✔
30Linear OA(4184, 4132, F4, 39) (dual of [4132, 3948, 40]-code) [i]✔
31Linear OA(4245, 4163, F4, 50) (dual of [4163, 3918, 51]-code) [i]✔
32Linear OA(4246, 4166, F4, 50) (dual of [4166, 3920, 51]-code) [i]✔
33Linear OA(4247, 4168, F4, 50) (dual of [4168, 3921, 51]-code) [i]✔
34Linear OA(4195, 4164, F4, 39) (dual of [4164, 3969, 40]-code) [i]✔
35Linear OA(4257, 4178, F4, 51) (dual of [4178, 3921, 52]-code) [i]✔
36Linear OA(4214, 4130, F4, 46) (dual of [4130, 3916, 47]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
37Linear OA(4208, 4126, F4, 45) (dual of [4126, 3918, 46]-code) [i]✔
38Linear OA(4207, 4124, F4, 45) (dual of [4124, 3917, 46]-code) [i]✔
39Linear OA(4206, 4122, F4, 45) (dual of [4122, 3916, 46]-code) [i]✔
40Linear OA(4207, 4129, F4, 44) (dual of [4129, 3922, 45]-code) [i]✔
41Linear OA(4197, 4114, F4, 43) (dual of [4114, 3917, 44]-code) [i]✔
42Linear OA(4199, 4121, F4, 43) (dual of [4121, 3922, 44]-code) [i]✔
43Linear OA(4189, 4105, F4, 42) (dual of [4105, 3916, 43]-code) [i]✔
44Linear OA(4183, 4105, F4, 41) (dual of [4105, 3922, 42]-code) [i]✔
45Linear OA(4179, 4114, F4, 39) (dual of [4114, 3935, 40]-code) [i]✔
46Linear OA(4178, 4112, F4, 39) (dual of [4112, 3934, 40]-code) [i]✔
47Linear OA(4181, 4121, F4, 39) (dual of [4121, 3940, 40]-code) [i]✔
48Linear OA(4183, 4129, F4, 39) (dual of [4129, 3946, 40]-code) [i]✔