Information on Result #616272

Linear OA(1634, 4096, F16, 12) (dual of [4096, 4062, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12

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(1640, 4113, F16, 12) (dual of [4113, 4073, 13]-code) [i](u, u+v)-Construction
2Linear OA(1641, 4120, F16, 12) (dual of [4120, 4079, 13]-code) [i]
3Linear OA(1642, 4129, F16, 12) (dual of [4129, 4087, 13]-code) [i]
4Linear OA(1643, 4134, F16, 12) (dual of [4134, 4091, 13]-code) [i]
5Linear OOA(1634, 2836, F16, 2, 12) (dual of [(2836, 2), 5638, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
6Digital (22, 34, 2836)-net over F16 [i]
7Linear OA(1643, 4106, F16, 12) (dual of [4106, 4063, 13]-code) [i](u, u−v, u+v+w)-Construction
8Linear OA(1637, 4099, F16, 13) (dual of [4099, 4062, 14]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
9Linear OA(1634, 4099, F16, 12) (dual of [4099, 4065, 13]-code) [i]✔
10Linear OA(1641, 4103, F16, 14) (dual of [4103, 4062, 15]-code) [i]✔
11Linear OA(1635, 4103, F16, 12) (dual of [4103, 4068, 13]-code) [i]✔
12Linear OA(1645, 4107, F16, 15) (dual of [4107, 4062, 16]-code) [i]✔
13Linear OA(1636, 4107, F16, 12) (dual of [4107, 4071, 13]-code) [i]✔
14Linear OA(1650, 4112, F16, 17) (dual of [4112, 4062, 18]-code) [i]✔
15Linear OA(1637, 4111, F16, 12) (dual of [4111, 4074, 13]-code) [i]✔
16Linear OA(1655, 4117, F16, 18) (dual of [4117, 4062, 19]-code) [i]✔
17Linear OA(1638, 4113, F16, 12) (dual of [4113, 4075, 13]-code) [i]✔
18Linear OA(1639, 4116, F16, 12) (dual of [4116, 4077, 13]-code) [i]✔
19Linear OA(1659, 4120, F16, 19) (dual of [4120, 4061, 20]-code) [i]✔
20Linear OA(1660, 4122, F16, 19) (dual of [4122, 4062, 20]-code) [i]✔
21Linear OA(1640, 4120, F16, 12) (dual of [4120, 4080, 13]-code) [i]✔
22Linear OA(1664, 4126, F16, 20) (dual of [4126, 4062, 21]-code) [i]✔
23Linear OA(1668, 4129, F16, 21) (dual of [4129, 4061, 22]-code) [i]✔
24Linear OA(1669, 4131, F16, 21) (dual of [4131, 4062, 22]-code) [i]✔
25Linear OA(1673, 4134, F16, 22) (dual of [4134, 4061, 23]-code) [i]✔
26Linear OA(1674, 4136, F16, 22) (dual of [4136, 4062, 23]-code) [i]✔
27Linear OA(1678, 4140, F16, 23) (dual of [4140, 4062, 24]-code) [i]✔
28Linear OA(1683, 4145, F16, 24) (dual of [4145, 4062, 25]-code) [i]✔
29Linear OA(1654, 4114, F16, 18) (dual of [4114, 4060, 19]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
30Linear OA(1651, 4114, F16, 17) (dual of [4114, 4063, 18]-code) [i]✔