Information on Result #613166

Linear OA(4187, 4096, F4, 42) (dual of [4096, 3909, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42

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(4208, 4118, F4, 42) (dual of [4118, 3910, 43]-code) [i](u, u+v)-Construction
2Linear OA(4213, 4124, F4, 42) (dual of [4124, 3911, 43]-code) [i]
3Linear OA(4214, 4126, F4, 42) (dual of [4126, 3912, 43]-code) [i]
4Linear OA(4215, 4128, F4, 42) (dual of [4128, 3913, 43]-code) [i]
5Linear OOA(4187, 3282, F4, 2, 42) (dual of [(3282, 2), 6377, 43]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
6Linear OOA(4187, 3282, F4, 3, 42) (dual of [(3282, 3), 9659, 43]-NRT-code) [i]
7Digital (145, 187, 3282)-net over F4 [i]
8Linear OA(4216, 4126, F4, 42) (dual of [4126, 3910, 43]-code) [i](u, u−v, u+v+w)-Construction
9Linear OA(4193, 4102, F4, 43) (dual of [4102, 3909, 44]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
10Linear OA(4187, 4102, F4, 42) (dual of [4102, 3915, 43]-code) [i]✔
11Linear OA(4200, 4109, F4, 44) (dual of [4109, 3909, 45]-code) [i]✔
12Linear OA(4202, 4111, F4, 45) (dual of [4111, 3909, 46]-code) [i]✔
13Linear OA(4190, 4111, F4, 42) (dual of [4111, 3921, 43]-code) [i]✔
14Linear OA(4209, 4113, F4, 46) (dual of [4113, 3904, 47]-code) [i]✔
15Linear OA(4210, 4119, F4, 46) (dual of [4119, 3909, 47]-code) [i]✔
16Linear OA(4191, 4113, F4, 42) (dual of [4113, 3922, 43]-code) [i]✔
17Linear OA(4192, 4119, F4, 42) (dual of [4119, 3927, 43]-code) [i]✔
18Linear OA(4218, 4127, F4, 47) (dual of [4127, 3909, 48]-code) [i]✔
19Linear OA(4194, 4127, F4, 42) (dual of [4127, 3933, 43]-code) [i]✔
20Linear OA(4230, 4139, F4, 49) (dual of [4139, 3909, 50]-code) [i]✔
21Linear OA(4227, 4136, F4, 48) (dual of [4136, 3909, 49]-code) [i]✔
22Linear OA(4200, 4139, F4, 42) (dual of [4139, 3939, 43]-code) [i]✔
23Linear OA(4239, 4148, F4, 50) (dual of [4148, 3909, 51]-code) [i]✔
24Linear OA(4203, 4148, F4, 42) (dual of [4148, 3945, 43]-code) [i]✔
25Linear OA(4247, 4156, F4, 51) (dual of [4156, 3909, 52]-code) [i]✔
26Linear OA(4205, 4156, F4, 42) (dual of [4156, 3951, 43]-code) [i]✔
27Linear OA(4254, 4161, F4, 52) (dual of [4161, 3907, 53]-code) [i]✔
28Linear OA(4257, 4166, F4, 52) (dual of [4166, 3909, 53]-code) [i]✔
29Linear OA(4213, 4170, F4, 42) (dual of [4170, 3957, 43]-code) [i]✔
30Linear OA(4216, 4179, F4, 42) (dual of [4179, 3963, 43]-code) [i]✔
31Linear OA(4226, 4132, F4, 48) (dual of [4132, 3906, 49]-code) [i]✔
32Linear OA(4257, 4163, F4, 53) (dual of [4163, 3906, 54]-code) [i]✔
33Linear OA(4258, 4166, F4, 53) (dual of [4166, 3908, 54]-code) [i]✔
34Linear OA(4259, 4168, F4, 53) (dual of [4168, 3909, 54]-code) [i]✔
35Linear OA(4255, 4164, F4, 52) (dual of [4164, 3909, 53]-code) [i]✔
36Linear OA(4209, 4163, F4, 42) (dual of [4163, 3954, 43]-code) [i]✔
37Linear OA(4210, 4166, F4, 42) (dual of [4166, 3956, 43]-code) [i]✔
38Linear OA(4211, 4168, F4, 42) (dual of [4168, 3957, 43]-code) [i]✔
39Linear OA(4215, 4178, F4, 42) (dual of [4178, 3963, 43]-code) [i]✔
40Linear OA(4217, 4121, F4, 47) (dual of [4121, 3904, 48]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
41Linear OA(4219, 4129, F4, 47) (dual of [4129, 3910, 48]-code) [i]✔
42Linear OA(4211, 4121, F4, 46) (dual of [4121, 3910, 47]-code) [i]✔
43Linear OA(4201, 4105, F4, 45) (dual of [4105, 3904, 46]-code) [i]✔
44Linear OA(4201, 4111, F4, 44) (dual of [4111, 3910, 45]-code) [i]✔
45Linear OA(4189, 4105, F4, 42) (dual of [4105, 3916, 43]-code) [i]✔
46Linear OA(4193, 4121, F4, 42) (dual of [4121, 3928, 43]-code) [i]✔
47Linear OA(4196, 4130, F4, 42) (dual of [4130, 3934, 43]-code) [i]✔