Information on Result #692083
Linear OA(1671, 4103, F16, 25) (dual of [4103, 4032, 26]-code), using construction X applied to Ce(24) ⊂ Ce(22) based on
- linear OA(1670, 4096, F16, 25) (dual of [4096, 4026, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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 [i]
- linear OA(161, 7, F16, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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(1689, 4168, F16, 25) (dual of [4168, 4079, 26]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(1671, 2893, F16, 2, 25) (dual of [(2893, 2), 5715, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (46, 71, 2893)-net over F16 | [i] | ||
| 4 | Linear OA(1674, 4127, F16, 25) (dual of [4127, 4053, 26]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(1675, 4192, F16, 25) (dual of [4192, 4117, 26]-code) | [i] | ||
| 6 | Linear OA(1676, 4394, F16, 25) (dual of [4394, 4318, 26]-code) | [i] | ||
| 7 | Linear OA(1677, 4806, F16, 25) (dual of [4806, 4729, 26]-code) | [i] | ||
| 8 | Linear OOA(1671, 2051, F16, 2, 25) (dual of [(2051, 2), 4031, 26]-NRT-code) | [i] | OOA Folding | |