Information on Result #616394

Linear OA(1664, 4096, F16, 23) (dual of [4096, 4032, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23

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(1675, 4113, F16, 23) (dual of [4113, 4038, 24]-code) [i](u, u+v)-Construction
2Linear OA(1676, 4120, F16, 23) (dual of [4120, 4044, 24]-code) [i]
3Linear OA(1677, 4129, F16, 23) (dual of [4129, 4052, 24]-code) [i]
4Linear OA(1678, 4134, F16, 23) (dual of [4134, 4056, 24]-code) [i]
5Linear OA(1679, 4141, F16, 23) (dual of [4141, 4062, 24]-code) [i]
6Linear OA(1680, 4145, F16, 23) (dual of [4145, 4065, 24]-code) [i]
7Linear OA(1681, 4161, F16, 23) (dual of [4161, 4080, 24]-code) [i]
8Linear OA(1681, 4114, F16, 23) (dual of [4114, 4033, 24]-code) [i]Generalized (u, u+v)-Construction
9Linear OOA(1664, 2359, F16, 2, 23) (dual of [(2359, 2), 4654, 24]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
10Digital (41, 64, 2359)-net over F16 [i]
11Linear OA(1679, 4112, F16, 23) (dual of [4112, 4033, 24]-code) [i](u, u−v, u+v+w)-Construction
12Linear OA(1680, 4114, F16, 23) (dual of [4114, 4034, 24]-code) [i]
13Linear OA(1681, 4116, F16, 23) (dual of [4116, 4035, 24]-code) [i]
14Linear OA(1667, 4099, F16, 24) (dual of [4099, 4032, 25]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
15Linear OA(1664, 4099, F16, 23) (dual of [4099, 4035, 24]-code) [i]✔
16Linear OA(1671, 4103, F16, 25) (dual of [4103, 4032, 26]-code) [i]✔
17Linear OA(1665, 4103, F16, 23) (dual of [4103, 4038, 24]-code) [i]✔
18Linear OA(1675, 4107, F16, 26) (dual of [4107, 4032, 27]-code) [i]✔
19Linear OA(1666, 4107, F16, 23) (dual of [4107, 4041, 24]-code) [i]✔
20Linear OA(1679, 4111, F16, 27) (dual of [4111, 4032, 28]-code) [i]✔
21Linear OA(1667, 4111, F16, 23) (dual of [4111, 4044, 24]-code) [i]✔
22Linear OA(1683, 4113, F16, 28) (dual of [4113, 4030, 29]-code) [i]✔
23Linear OA(1684, 4116, F16, 28) (dual of [4116, 4032, 29]-code) [i]✔
24Linear OA(1668, 4113, F16, 23) (dual of [4113, 4045, 24]-code) [i]✔
25Linear OA(1669, 4116, F16, 23) (dual of [4116, 4047, 24]-code) [i]✔
26Linear OA(1688, 4120, F16, 29) (dual of [4120, 4032, 30]-code) [i]✔
27Linear OA(1670, 4120, F16, 23) (dual of [4120, 4050, 24]-code) [i]✔
28Linear OA(1693, 4125, F16, 30) (dual of [4125, 4032, 31]-code) [i]✔
29Linear OA(1673, 4126, F16, 23) (dual of [4126, 4053, 24]-code) [i]✔
30Linear OA(1697, 4129, F16, 31) (dual of [4129, 4032, 32]-code) [i]✔
31Linear OA(1674, 4129, F16, 23) (dual of [4129, 4055, 24]-code) [i]✔
32Linear OA(1675, 4131, F16, 23) (dual of [4131, 4056, 24]-code) [i]✔
33Linear OA(16103, 4134, F16, 33) (dual of [4134, 4031, 34]-code) [i]✔
34Linear OA(16104, 4136, F16, 33) (dual of [4136, 4032, 34]-code) [i]✔
35Linear OA(16102, 4134, F16, 32) (dual of [4134, 4032, 33]-code) [i]✔
36Linear OA(1676, 4134, F16, 23) (dual of [4134, 4058, 24]-code) [i]✔
37Linear OA(1677, 4136, F16, 23) (dual of [4136, 4059, 24]-code) [i]✔
38Linear OA(16108, 4140, F16, 34) (dual of [4140, 4032, 35]-code) [i]✔
39Linear OA(1678, 4140, F16, 23) (dual of [4140, 4062, 24]-code) [i]✔
40Linear OA(16113, 4145, F16, 35) (dual of [4145, 4032, 36]-code) [i]✔
41Linear OA(16118, 4150, F16, 36) (dual of [4150, 4032, 37]-code) [i]✔
42Linear OA(16122, 4154, F16, 37) (dual of [4154, 4032, 38]-code) [i]✔
43Linear OA(16126, 4158, F16, 38) (dual of [4158, 4032, 39]-code) [i]✔
44Linear OA(16130, 4161, F16, 39) (dual of [4161, 4031, 40]-code) [i]✔