Information on Result #1314119
Linear OA(16121, 4138, F16, 42) (dual of [4138, 4017, 43]-code), using 36 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0, 1, 28 times 0) based on linear OA(16118, 4099, F16, 42) (dual of [4099, 3981, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(40) [i] based on
- linear OA(16118, 4096, F16, 42) (dual of [4096, 3978, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(16115, 4096, F16, 41) (dual of [4096, 3981, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(16121, 4138, F16, 2, 42) (dual of [(4138, 2), 8155, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (79, 121, 4138)-net over F16 | [i] | ||
| 3 | Linear OOA(16121, 2069, F16, 2, 42) (dual of [(2069, 2), 4017, 43]-NRT-code) | [i] | OOA Folding | |