Information on Result #616415

Linear OA(1670, 4096, F16, 25) (dual of [4096, 4026, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25

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(1682, 4113, F16, 25) (dual of [4113, 4031, 26]-code) [i](u, u+v)-Construction
2Linear OA(1683, 4120, F16, 25) (dual of [4120, 4037, 26]-code) [i]
3Linear OA(1684, 4129, F16, 25) (dual of [4129, 4045, 26]-code) [i]
4Linear OA(1685, 4134, F16, 25) (dual of [4134, 4049, 26]-code) [i]
5Linear OA(1686, 4141, F16, 25) (dual of [4141, 4055, 26]-code) [i]
6Linear OA(1687, 4145, F16, 25) (dual of [4145, 4058, 26]-code) [i]
7Linear OA(1688, 4161, F16, 25) (dual of [4161, 4073, 26]-code) [i]
8Linear OA(1689, 4163, F16, 25) (dual of [4163, 4074, 26]-code) [i]
9Linear OOA(1670, 2563, F16, 2, 25) (dual of [(2563, 2), 5056, 26]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
10Digital (45, 70, 2563)-net over F16 [i]
11Linear OA(1687, 4114, F16, 25) (dual of [4114, 4027, 26]-code) [i](u, u−v, u+v+w)-Construction
12Linear OA(1688, 4116, F16, 25) (dual of [4116, 4028, 26]-code) [i]
13Linear OA(1689, 4118, F16, 25) (dual of [4118, 4029, 26]-code) [i]
14Linear OA(1673, 4099, F16, 26) (dual of [4099, 4026, 27]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
15Linear OA(1670, 4099, F16, 25) (dual of [4099, 4029, 26]-code) [i]✔
16Linear OA(1677, 4103, F16, 27) (dual of [4103, 4026, 28]-code) [i]✔
17Linear OA(1671, 4103, F16, 25) (dual of [4103, 4032, 26]-code) [i]✔
18Linear OA(1681, 4107, F16, 28) (dual of [4107, 4026, 29]-code) [i]✔
19Linear OA(1672, 4107, F16, 25) (dual of [4107, 4035, 26]-code) [i]✔
20Linear OA(1685, 4111, F16, 29) (dual of [4111, 4026, 30]-code) [i]✔
21Linear OA(1673, 4111, F16, 25) (dual of [4111, 4038, 26]-code) [i]✔
22Linear OA(1689, 4113, F16, 30) (dual of [4113, 4024, 31]-code) [i]✔
23Linear OA(1690, 4116, F16, 30) (dual of [4116, 4026, 31]-code) [i]✔
24Linear OA(1674, 4113, F16, 25) (dual of [4113, 4039, 26]-code) [i]✔
25Linear OA(1675, 4116, F16, 25) (dual of [4116, 4041, 26]-code) [i]✔
26Linear OA(1694, 4120, F16, 31) (dual of [4120, 4026, 32]-code) [i]✔
27Linear OA(1676, 4120, F16, 25) (dual of [4120, 4044, 26]-code) [i]✔
28Linear OA(16100, 4126, F16, 33) (dual of [4126, 4026, 34]-code) [i]✔
29Linear OA(1678, 4125, F16, 25) (dual of [4125, 4047, 26]-code) [i]✔
30Linear OA(16104, 4129, F16, 34) (dual of [4129, 4025, 35]-code) [i]✔
31Linear OA(16105, 4131, F16, 34) (dual of [4131, 4026, 35]-code) [i]✔
32Linear OA(1679, 4129, F16, 25) (dual of [4129, 4050, 26]-code) [i]✔
33Linear OA(16109, 4134, F16, 35) (dual of [4134, 4025, 36]-code) [i]✔
34Linear OA(16110, 4136, F16, 35) (dual of [4136, 4026, 36]-code) [i]✔
35Linear OA(1682, 4134, F16, 25) (dual of [4134, 4052, 26]-code) [i]✔
36Linear OA(1683, 4136, F16, 25) (dual of [4136, 4053, 26]-code) [i]✔
37Linear OA(16114, 4140, F16, 36) (dual of [4140, 4026, 37]-code) [i]✔
38Linear OA(1684, 4140, F16, 25) (dual of [4140, 4056, 26]-code) [i]✔
39Linear OA(16119, 4145, F16, 37) (dual of [4145, 4026, 38]-code) [i]✔
40Linear OA(1686, 4145, F16, 25) (dual of [4145, 4059, 26]-code) [i]✔
41Linear OA(16124, 4150, F16, 38) (dual of [4150, 4026, 39]-code) [i]✔
42Linear OA(16128, 4154, F16, 39) (dual of [4154, 4026, 40]-code) [i]✔