Information on Result #616466

Linear OA(1688, 4096, F16, 31) (dual of [4096, 4008, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, 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(16103, 4114, F16, 31) (dual of [4114, 4011, 32]-code) [i](u, u+v)-Construction
2Linear OA(16104, 4120, F16, 31) (dual of [4120, 4016, 32]-code) [i]
3Linear OA(16105, 4129, F16, 31) (dual of [4129, 4024, 32]-code) [i]
4Linear OA(16106, 4134, F16, 31) (dual of [4134, 4028, 32]-code) [i]
5Linear OA(16107, 4141, F16, 31) (dual of [4141, 4034, 32]-code) [i]
6Linear OA(16108, 4145, F16, 31) (dual of [4145, 4037, 32]-code) [i]
7Linear OA(16109, 4161, F16, 31) (dual of [4161, 4052, 32]-code) [i]
8Linear OA(16110, 4163, F16, 31) (dual of [4163, 4053, 32]-code) [i]
9Linear OA(16111, 4165, F16, 31) (dual of [4165, 4054, 32]-code) [i]
10Linear OA(16112, 4167, F16, 31) (dual of [4167, 4055, 32]-code) [i]
11Linear OA(16113, 4169, F16, 31) (dual of [4169, 4056, 32]-code) [i]
12Linear OA(16111, 4120, F16, 31) (dual of [4120, 4009, 32]-code) [i]Generalized (u, u+v)-Construction
13Linear OA(16113, 4123, F16, 31) (dual of [4123, 4010, 32]-code) [i]
14Linear OOA(1688, 3172, F16, 2, 31) (dual of [(3172, 2), 6256, 32]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
15Digital (57, 88, 3172)-net over F16 [i]
16Linear OA(16109, 4118, F16, 31) (dual of [4118, 4009, 32]-code) [i](u, u−v, u+v+w)-Construction
17Linear OA(16110, 4120, F16, 31) (dual of [4120, 4010, 32]-code) [i]
18Linear OA(16111, 4122, F16, 31) (dual of [4122, 4011, 32]-code) [i]
19Linear OA(16112, 4124, F16, 31) (dual of [4124, 4012, 32]-code) [i]
20Linear OA(16113, 4131, F16, 31) (dual of [4131, 4018, 32]-code) [i]
21Linear OA(1692, 4100, F16, 33) (dual of [4100, 4008, 34]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
22Linear OA(1688, 4099, F16, 31) (dual of [4099, 4011, 32]-code) [i]✔
23Linear OA(1696, 4104, F16, 34) (dual of [4104, 4008, 35]-code) [i]✔
24Linear OA(1689, 4103, F16, 31) (dual of [4103, 4014, 32]-code) [i]✔
25Linear OA(16100, 4108, F16, 35) (dual of [4108, 4008, 36]-code) [i]✔
26Linear OA(1690, 4107, F16, 31) (dual of [4107, 4017, 32]-code) [i]✔
27Linear OA(16104, 4112, F16, 36) (dual of [4112, 4008, 37]-code) [i]✔
28Linear OA(1691, 4111, F16, 31) (dual of [4111, 4020, 32]-code) [i]✔
29Linear OA(16109, 4117, F16, 37) (dual of [4117, 4008, 38]-code) [i]✔
30Linear OA(1692, 4113, F16, 31) (dual of [4113, 4021, 32]-code) [i]✔
31Linear OA(1693, 4116, F16, 31) (dual of [4116, 4023, 32]-code) [i]✔
32Linear OA(16113, 4120, F16, 38) (dual of [4120, 4007, 39]-code) [i]✔
33Linear OA(16114, 4122, F16, 38) (dual of [4122, 4008, 39]-code) [i]✔
34Linear OA(1694, 4120, F16, 31) (dual of [4120, 4026, 32]-code) [i]✔
35Linear OA(16118, 4126, F16, 39) (dual of [4126, 4008, 40]-code) [i]✔
36Linear OA(1696, 4125, F16, 31) (dual of [4125, 4029, 32]-code) [i]✔
37Linear OA(16122, 4129, F16, 40) (dual of [4129, 4007, 41]-code) [i]✔
38Linear OA(16123, 4131, F16, 40) (dual of [4131, 4008, 41]-code) [i]✔
39Linear OA(1697, 4129, F16, 31) (dual of [4129, 4032, 32]-code) [i]✔
40Linear OA(16127, 4134, F16, 41) (dual of [4134, 4007, 42]-code) [i]✔
41Linear OA(16128, 4136, F16, 41) (dual of [4136, 4008, 42]-code) [i]✔
42Linear OA(1699, 4134, F16, 31) (dual of [4134, 4035, 32]-code) [i]✔
43Linear OA(16101, 4139, F16, 31) (dual of [4139, 4038, 32]-code) [i]✔
44Linear OA(16102, 4141, F16, 31) (dual of [4141, 4039, 32]-code) [i]✔
45Linear OA(16103, 4144, F16, 31) (dual of [4144, 4041, 32]-code) [i]✔
46Linear OA(16105, 4149, F16, 31) (dual of [4149, 4044, 32]-code) [i]✔
47Linear OA(16106, 4153, F16, 31) (dual of [4153, 4047, 32]-code) [i]✔
48Linear OA(16107, 4157, F16, 31) (dual of [4157, 4050, 32]-code) [i]✔
49Linear OA(16105, 4114, F16, 36) (dual of [4114, 4009, 37]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes