Information on Result #616341

Linear OA(1649, 4096, F16, 18) (dual of [4096, 4047, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18

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(1658, 4113, F16, 18) (dual of [4113, 4055, 19]-code) [i](u, u+v)-Construction
2Linear OA(1659, 4120, F16, 18) (dual of [4120, 4061, 19]-code) [i]
3Linear OA(1660, 4129, F16, 18) (dual of [4129, 4069, 19]-code) [i]
4Linear OA(1661, 4134, F16, 18) (dual of [4134, 4073, 19]-code) [i]
5Linear OA(1662, 4141, F16, 18) (dual of [4141, 4079, 19]-code) [i]
6Linear OA(1663, 4145, F16, 18) (dual of [4145, 4082, 19]-code) [i]
7Linear OA(1663, 4111, F16, 18) (dual of [4111, 4048, 19]-code) [i]Generalized (u, u+v)-Construction
8Linear OA(1662, 4110, F16, 18) (dual of [4110, 4048, 19]-code) [i](u, u−v, u+v+w)-Construction
9Linear OA(1663, 4112, F16, 18) (dual of [4112, 4049, 19]-code) [i]
10Linear OA(1652, 4099, F16, 19) (dual of [4099, 4047, 20]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
11Linear OA(1649, 4099, F16, 18) (dual of [4099, 4050, 19]-code) [i]✔
12Linear OA(1656, 4103, F16, 20) (dual of [4103, 4047, 21]-code) [i]✔
13Linear OA(1651, 4104, F16, 18) (dual of [4104, 4053, 19]-code) [i]✔
14Linear OA(1660, 4107, F16, 21) (dual of [4107, 4047, 22]-code) [i]✔
15Linear OA(1652, 4108, F16, 18) (dual of [4108, 4056, 19]-code) [i]✔
16Linear OA(1664, 4111, F16, 22) (dual of [4111, 4047, 23]-code) [i]✔
17Linear OA(1653, 4112, F16, 18) (dual of [4112, 4059, 19]-code) [i]✔
18Linear OA(1668, 4113, F16, 23) (dual of [4113, 4045, 24]-code) [i]✔
19Linear OA(1669, 4116, F16, 23) (dual of [4116, 4047, 24]-code) [i]✔
20Linear OA(1655, 4117, F16, 18) (dual of [4117, 4062, 19]-code) [i]✔
21Linear OA(1673, 4120, F16, 24) (dual of [4120, 4047, 25]-code) [i]✔
22Linear OA(1656, 4120, F16, 18) (dual of [4120, 4064, 19]-code) [i]✔
23Linear OA(1657, 4122, F16, 18) (dual of [4122, 4065, 19]-code) [i]✔
24Linear OA(1678, 4125, F16, 25) (dual of [4125, 4047, 26]-code) [i]✔
25Linear OA(1658, 4126, F16, 18) (dual of [4126, 4068, 19]-code) [i]✔
26Linear OA(1682, 4129, F16, 26) (dual of [4129, 4047, 27]-code) [i]✔
27Linear OA(1659, 4129, F16, 18) (dual of [4129, 4070, 19]-code) [i]✔
28Linear OA(1660, 4131, F16, 18) (dual of [4131, 4071, 19]-code) [i]✔
29Linear OA(1687, 4134, F16, 27) (dual of [4134, 4047, 28]-code) [i]✔
30Linear OA(1692, 4139, F16, 28) (dual of [4139, 4047, 29]-code) [i]✔
31Linear OA(1696, 4141, F16, 29) (dual of [4141, 4045, 30]-code) [i]✔
32Linear OA(1697, 4144, F16, 29) (dual of [4144, 4047, 30]-code) [i]✔
33Linear OA(16102, 4149, F16, 30) (dual of [4149, 4047, 31]-code) [i]✔
34Linear OA(16106, 4153, F16, 31) (dual of [4153, 4047, 32]-code) [i]✔
35Linear OA(16111, 4158, F16, 33) (dual of [4158, 4047, 34]-code) [i]✔
36Linear OA(16115, 4161, F16, 34) (dual of [4161, 4046, 35]-code) [i]✔
37Linear OA(16116, 4163, F16, 34) (dual of [4163, 4047, 35]-code) [i]✔
38Linear OA(16122, 4167, F16, 35) (dual of [4167, 4045, 36]-code) [i]✔
39Linear OA(16123, 4169, F16, 35) (dual of [4169, 4046, 36]-code) [i]✔
40Linear OA(16124, 4171, F16, 35) (dual of [4171, 4047, 36]-code) [i]✔
41Linear OA(1654, 4114, F16, 18) (dual of [4114, 4060, 19]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes