Information on Result #616333
Linear OA(1646, 4096, F16, 17) (dual of [4096, 4050, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(1645, 4095, F16, 16) (dual of [4095, 4050, 17]-code) | [i] | Truncation | |
| 2 | Linear OA(1654, 4113, F16, 17) (dual of [4113, 4059, 18]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1655, 4120, F16, 17) (dual of [4120, 4065, 18]-code) | [i] | ||
| 4 | Linear OA(1656, 4129, F16, 17) (dual of [4129, 4073, 18]-code) | [i] | ||
| 5 | Linear OA(1657, 4134, F16, 17) (dual of [4134, 4077, 18]-code) | [i] | ||
| 6 | Linear OA(1658, 4141, F16, 17) (dual of [4141, 4083, 18]-code) | [i] | ||
| 7 | Linear OA(1659, 4147, F16, 17) (dual of [4147, 4088, 18]-code) | [i] | ||
| 8 | Linear OA(1659, 4149, F16, 17) (dual of [4149, 4090, 18]-code) | [i] | ||
| 9 | Linear OA(1657, 4108, F16, 17) (dual of [4108, 4051, 18]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 10 | Linear OA(1658, 4110, F16, 17) (dual of [4110, 4052, 18]-code) | [i] | ||
| 11 | Linear OA(1659, 4130, F16, 17) (dual of [4130, 4071, 18]-code) | [i] | ||
| 12 | Linear OA(1650, 4120, F16, 17) (dual of [4120, 4070, 18]-code) | [i] | Varšamov–Edel Lengthening | |
| 13 | Linear OA(1651, 4177, F16, 17) (dual of [4177, 4126, 18]-code) | [i] | ||
| 14 | Linear OA(1652, 4335, F16, 17) (dual of [4335, 4283, 18]-code) | [i] | ||
| 15 | Linear OA(1653, 4692, F16, 17) (dual of [4692, 4639, 18]-code) | [i] | ||
| 16 | Linear OA(1654, 5339, F16, 17) (dual of [5339, 5285, 18]-code) | [i] | ||
| 17 | Linear OA(1649, 4099, F16, 18) (dual of [4099, 4050, 19]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 18 | Linear OA(1647, 4100, F16, 17) (dual of [4100, 4053, 18]-code) | [i] | ✔ | |
| 19 | Linear OA(1653, 4103, F16, 19) (dual of [4103, 4050, 20]-code) | [i] | ✔ | |
| 20 | Linear OA(1648, 4104, F16, 17) (dual of [4104, 4056, 18]-code) | [i] | ✔ | |
| 21 | Linear OA(1657, 4107, F16, 20) (dual of [4107, 4050, 21]-code) | [i] | ✔ | |
| 22 | Linear OA(1649, 4108, F16, 17) (dual of [4108, 4059, 18]-code) | [i] | ✔ | |
| 23 | Linear OA(1661, 4111, F16, 21) (dual of [4111, 4050, 22]-code) | [i] | ✔ | |
| 24 | Linear OA(1650, 4112, F16, 17) (dual of [4112, 4062, 18]-code) | [i] | ✔ | |
| 25 | Linear OA(1665, 4113, F16, 22) (dual of [4113, 4048, 23]-code) | [i] | ✔ | |
| 26 | Linear OA(1666, 4116, F16, 22) (dual of [4116, 4050, 23]-code) | [i] | ✔ | |
| 27 | Linear OA(1652, 4117, F16, 17) (dual of [4117, 4065, 18]-code) | [i] | ✔ | |
| 28 | Linear OA(1650, 4113, F16, 16) (dual of [4113, 4063, 17]-code) | [i] | ✔ | |
| 29 | Linear OA(1670, 4120, F16, 23) (dual of [4120, 4050, 24]-code) | [i] | ✔ | |
| 30 | Linear OA(1653, 4120, F16, 17) (dual of [4120, 4067, 18]-code) | [i] | ✔ | |
| 31 | Linear OA(1654, 4122, F16, 17) (dual of [4122, 4068, 18]-code) | [i] | ✔ | |
| 32 | Linear OA(1652, 4120, F16, 16) (dual of [4120, 4068, 17]-code) | [i] | ✔ | |
| 33 | Linear OA(1675, 4125, F16, 24) (dual of [4125, 4050, 25]-code) | [i] | ✔ | |
| 34 | Linear OA(1655, 4126, F16, 17) (dual of [4126, 4071, 18]-code) | [i] | ✔ | |
| 35 | Linear OA(1679, 4129, F16, 25) (dual of [4129, 4050, 26]-code) | [i] | ✔ | |
| 36 | Linear OA(1655, 4129, F16, 16) (dual of [4129, 4074, 17]-code) | [i] | ✔ | |
| 37 | Linear OA(1684, 4134, F16, 26) (dual of [4134, 4050, 27]-code) | [i] | ✔ | |
| 38 | Linear OA(1689, 4139, F16, 27) (dual of [4139, 4050, 28]-code) | [i] | ✔ | |
| 39 | Linear OA(1693, 4141, F16, 28) (dual of [4141, 4048, 29]-code) | [i] | ✔ | |
| 40 | Linear OA(1694, 4144, F16, 28) (dual of [4144, 4050, 29]-code) | [i] | ✔ | |
| 41 | Linear OA(1699, 4149, F16, 29) (dual of [4149, 4050, 30]-code) | [i] | ✔ | |
| 42 | Linear OA(16103, 4153, F16, 30) (dual of [4153, 4050, 31]-code) | [i] | ✔ | |
| 43 | Linear OA(16107, 4157, F16, 31) (dual of [4157, 4050, 32]-code) | [i] | ✔ | |
| 44 | Linear OA(16112, 4161, F16, 33) (dual of [4161, 4049, 34]-code) | [i] | ✔ | |
| 45 | Linear OA(16113, 4163, F16, 33) (dual of [4163, 4050, 34]-code) | [i] | ✔ | |
| 46 | Linear OA(16111, 4161, F16, 32) (dual of [4161, 4050, 33]-code) | [i] | ✔ | |
| 47 | Linear OA(16119, 4167, F16, 34) (dual of [4167, 4048, 35]-code) | [i] | ✔ | |
| 48 | Linear OA(16120, 4169, F16, 34) (dual of [4169, 4049, 35]-code) | [i] | ✔ | |
| 49 | Linear OA(16121, 4171, F16, 34) (dual of [4171, 4050, 35]-code) | [i] | ✔ | |
| 50 | Linear OA(1663, 4114, F16, 21) (dual of [4114, 4051, 22]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 51 | Linear OA(1651, 4114, F16, 17) (dual of [4114, 4063, 18]-code) | [i] | ✔ | |
| 52 | Linear OOA(1646, 2048, F16, 2, 17) (dual of [(2048, 2), 4050, 18]-NRT-code) | [i] | OOA Folding | |