Information on Result #616460

Linear OA(1685, 4096, F16, 30) (dual of [4096, 4011, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30

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(16100, 4114, F16, 30) (dual of [4114, 4014, 31]-code) [i](u, u+v)-Construction
2Linear OA(16101, 4120, F16, 30) (dual of [4120, 4019, 31]-code) [i]
3Linear OA(16102, 4129, F16, 30) (dual of [4129, 4027, 31]-code) [i]
4Linear OA(16103, 4134, F16, 30) (dual of [4134, 4031, 31]-code) [i]
5Linear OA(16104, 4141, F16, 30) (dual of [4141, 4037, 31]-code) [i]
6Linear OA(16105, 4145, F16, 30) (dual of [4145, 4040, 31]-code) [i]
7Linear OA(16106, 4161, F16, 30) (dual of [4161, 4055, 31]-code) [i]
8Linear OA(16107, 4163, F16, 30) (dual of [4163, 4056, 31]-code) [i]
9Linear OA(16108, 4165, F16, 30) (dual of [4165, 4057, 31]-code) [i]
10Linear OA(16109, 4167, F16, 30) (dual of [4167, 4058, 31]-code) [i]
11Linear OA(16108, 4120, F16, 30) (dual of [4120, 4012, 31]-code) [i]Generalized (u, u+v)-Construction
12Linear OOA(1685, 3071, F16, 2, 30) (dual of [(3071, 2), 6057, 31]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
13Digital (55, 85, 3071)-net over F16 [i]
14Linear OA(16106, 4118, F16, 30) (dual of [4118, 4012, 31]-code) [i](u, u−v, u+v+w)-Construction
15Linear OA(16107, 4120, F16, 30) (dual of [4120, 4013, 31]-code) [i]
16Linear OA(16108, 4122, F16, 30) (dual of [4122, 4014, 31]-code) [i]
17Linear OA(16109, 4124, F16, 30) (dual of [4124, 4015, 31]-code) [i]
18Linear OA(1688, 4099, F16, 31) (dual of [4099, 4011, 32]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
19Linear OA(1685, 4099, F16, 30) (dual of [4099, 4014, 31]-code) [i]✔
20Linear OA(1693, 4104, F16, 33) (dual of [4104, 4011, 34]-code) [i]✔
21Linear OA(1686, 4103, F16, 30) (dual of [4103, 4017, 31]-code) [i]✔
22Linear OA(1697, 4108, F16, 34) (dual of [4108, 4011, 35]-code) [i]✔
23Linear OA(1687, 4107, F16, 30) (dual of [4107, 4020, 31]-code) [i]✔
24Linear OA(16101, 4112, F16, 35) (dual of [4112, 4011, 36]-code) [i]✔
25Linear OA(1688, 4111, F16, 30) (dual of [4111, 4023, 31]-code) [i]✔
26Linear OA(16106, 4117, F16, 36) (dual of [4117, 4011, 37]-code) [i]✔
27Linear OA(1689, 4113, F16, 30) (dual of [4113, 4024, 31]-code) [i]✔
28Linear OA(1690, 4116, F16, 30) (dual of [4116, 4026, 31]-code) [i]✔
29Linear OA(16110, 4120, F16, 37) (dual of [4120, 4010, 38]-code) [i]✔
30Linear OA(16111, 4122, F16, 37) (dual of [4122, 4011, 38]-code) [i]✔
31Linear OA(1691, 4120, F16, 30) (dual of [4120, 4029, 31]-code) [i]✔
32Linear OA(16115, 4126, F16, 38) (dual of [4126, 4011, 39]-code) [i]✔
33Linear OA(1693, 4125, F16, 30) (dual of [4125, 4032, 31]-code) [i]✔
34Linear OA(16119, 4129, F16, 39) (dual of [4129, 4010, 40]-code) [i]✔
35Linear OA(16120, 4131, F16, 39) (dual of [4131, 4011, 40]-code) [i]✔
36Linear OA(1694, 4129, F16, 30) (dual of [4129, 4035, 31]-code) [i]✔
37Linear OA(16124, 4134, F16, 40) (dual of [4134, 4010, 41]-code) [i]✔
38Linear OA(16125, 4136, F16, 40) (dual of [4136, 4011, 41]-code) [i]✔
39Linear OA(1696, 4134, F16, 30) (dual of [4134, 4038, 31]-code) [i]✔
40Linear OA(16129, 4140, F16, 41) (dual of [4140, 4011, 42]-code) [i]✔
41Linear OA(1698, 4139, F16, 30) (dual of [4139, 4041, 31]-code) [i]✔
42Linear OA(1699, 4141, F16, 30) (dual of [4141, 4042, 31]-code) [i]✔
43Linear OA(16100, 4144, F16, 30) (dual of [4144, 4044, 31]-code) [i]✔
44Linear OA(16102, 4149, F16, 30) (dual of [4149, 4047, 31]-code) [i]✔
45Linear OA(16103, 4153, F16, 30) (dual of [4153, 4050, 31]-code) [i]✔
46Linear OA(16105, 4158, F16, 30) (dual of [4158, 4053, 31]-code) [i]✔
47Linear OA(16105, 4114, F16, 36) (dual of [4114, 4009, 37]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes