Information on Result #616357

Linear OA(1655, 4096, F16, 20) (dual of [4096, 4041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20

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(1665, 4113, F16, 20) (dual of [4113, 4048, 21]-code) [i](u, u+v)-Construction
2Linear OA(1666, 4120, F16, 20) (dual of [4120, 4054, 21]-code) [i]
3Linear OA(1667, 4129, F16, 20) (dual of [4129, 4062, 21]-code) [i]
4Linear OA(1668, 4134, F16, 20) (dual of [4134, 4066, 21]-code) [i]
5Linear OA(1669, 4141, F16, 20) (dual of [4141, 4072, 21]-code) [i]
6Linear OOA(1655, 2053, F16, 2, 20) (dual of [(2053, 2), 4051, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
7Digital (35, 55, 2053)-net over F16 [i]
8Linear OA(1668, 4110, F16, 20) (dual of [4110, 4042, 21]-code) [i](u, u−v, u+v+w)-Construction
9Linear OA(1669, 4112, F16, 20) (dual of [4112, 4043, 21]-code) [i]
10Linear OA(1658, 4099, F16, 21) (dual of [4099, 4041, 22]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
11Linear OA(1655, 4099, F16, 20) (dual of [4099, 4044, 21]-code) [i]✔
12Linear OA(1662, 4103, F16, 22) (dual of [4103, 4041, 23]-code) [i]✔
13Linear OA(1656, 4103, F16, 20) (dual of [4103, 4047, 21]-code) [i]✔
14Linear OA(1666, 4107, F16, 23) (dual of [4107, 4041, 24]-code) [i]✔
15Linear OA(1657, 4107, F16, 20) (dual of [4107, 4050, 21]-code) [i]✔
16Linear OA(1670, 4111, F16, 24) (dual of [4111, 4041, 25]-code) [i]✔
17Linear OA(1659, 4112, F16, 20) (dual of [4112, 4053, 21]-code) [i]✔
18Linear OA(1674, 4113, F16, 25) (dual of [4113, 4039, 26]-code) [i]✔
19Linear OA(1675, 4116, F16, 25) (dual of [4116, 4041, 26]-code) [i]✔
20Linear OA(1661, 4117, F16, 20) (dual of [4117, 4056, 21]-code) [i]✔
21Linear OA(1679, 4120, F16, 26) (dual of [4120, 4041, 27]-code) [i]✔
22Linear OA(1662, 4120, F16, 20) (dual of [4120, 4058, 21]-code) [i]✔
23Linear OA(1663, 4122, F16, 20) (dual of [4122, 4059, 21]-code) [i]✔
24Linear OA(1684, 4125, F16, 27) (dual of [4125, 4041, 28]-code) [i]✔
25Linear OA(1664, 4126, F16, 20) (dual of [4126, 4062, 21]-code) [i]✔
26Linear OA(1688, 4129, F16, 28) (dual of [4129, 4041, 29]-code) [i]✔
27Linear OA(1665, 4129, F16, 20) (dual of [4129, 4064, 21]-code) [i]✔
28Linear OA(1666, 4131, F16, 20) (dual of [4131, 4065, 21]-code) [i]✔
29Linear OA(1693, 4134, F16, 29) (dual of [4134, 4041, 30]-code) [i]✔
30Linear OA(1667, 4134, F16, 20) (dual of [4134, 4067, 21]-code) [i]✔
31Linear OA(1668, 4136, F16, 20) (dual of [4136, 4068, 21]-code) [i]✔
32Linear OA(1698, 4139, F16, 30) (dual of [4139, 4041, 31]-code) [i]✔
33Linear OA(16102, 4141, F16, 31) (dual of [4141, 4039, 32]-code) [i]✔
34Linear OA(16103, 4144, F16, 31) (dual of [4144, 4041, 32]-code) [i]✔
35Linear OA(16109, 4150, F16, 33) (dual of [4150, 4041, 34]-code) [i]✔
36Linear OA(16113, 4154, F16, 34) (dual of [4154, 4041, 35]-code) [i]✔
37Linear OA(16117, 4158, F16, 35) (dual of [4158, 4041, 36]-code) [i]✔
38Linear OA(16121, 4161, F16, 36) (dual of [4161, 4040, 37]-code) [i]✔
39Linear OA(16122, 4163, F16, 36) (dual of [4163, 4041, 37]-code) [i]✔
40Linear OA(16128, 4167, F16, 37) (dual of [4167, 4039, 38]-code) [i]✔
41Linear OA(16129, 4169, F16, 37) (dual of [4169, 4040, 38]-code) [i]✔
42Linear OA(16130, 4171, F16, 37) (dual of [4171, 4041, 38]-code) [i]✔
43Linear OA(1660, 4114, F16, 20) (dual of [4114, 4054, 21]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes