Information on Result #1314084
Linear OA(16116, 4161, F16, 40) (dual of [4161, 4045, 41]-code), using 58 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 10 times 0, 1, 43 times 0) based on linear OA(16112, 4099, F16, 40) (dual of [4099, 3987, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(38) [i] based on
- linear OA(16112, 4096, F16, 40) (dual of [4096, 3984, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(16109, 4096, F16, 39) (dual of [4096, 3987, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(160, 3, F16, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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 OOA(16116, 4161, F16, 2, 40) (dual of [(4161, 2), 8206, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (76, 116, 4161)-net over F16 | [i] | ||
| 3 | Linear OOA(16116, 2080, F16, 2, 40) (dual of [(2080, 2), 4044, 41]-NRT-code) | [i] | OOA Folding | |