Information on Result #692077
Linear OA(1689, 4103, F16, 31) (dual of [4103, 4014, 32]-code), using construction X applied to Ce(30) ⊂ Ce(28) based on
- linear OA(1688, 4096, F16, 31) (dual of [4096, 4008, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(1682, 4096, F16, 29) (dual of [4096, 4014, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(16110, 4168, F16, 31) (dual of [4168, 4058, 32]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(16111, 4170, F16, 31) (dual of [4170, 4059, 32]-code) | [i] | ||
| 3 | Linear OA(16112, 4172, F16, 31) (dual of [4172, 4060, 32]-code) | [i] | ||
| 4 | Linear OA(16113, 4174, F16, 31) (dual of [4174, 4061, 32]-code) | [i] | ||
| 5 | Linear OOA(1689, 3492, F16, 2, 31) (dual of [(3492, 2), 6895, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (58, 89, 3492)-net over F16 | [i] | ||
| 7 | Linear OOA(1689, 2051, F16, 2, 31) (dual of [(2051, 2), 4013, 32]-NRT-code) | [i] | OOA Folding | |