Information on Result #1314147
Linear OA(16126, 4113, F16, 44) (dual of [4113, 3987, 45]-code), using 12 step Varšamov–Edel lengthening with (ri) = (2, 11 times 0) based on linear OA(16124, 4099, F16, 44) (dual of [4099, 3975, 45]-code), using
- construction X applied to Ce(43) ⊂ Ce(42) [i] based on
- linear OA(16124, 4096, F16, 44) (dual of [4096, 3972, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(16121, 4096, F16, 43) (dual of [4096, 3975, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [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(16126, 4113, F16, 2, 44) (dual of [(4113, 2), 8100, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (82, 126, 4113)-net over F16 | [i] | ||
| 3 | Linear OOA(16126, 2056, F16, 2, 44) (dual of [(2056, 2), 3986, 45]-NRT-code) | [i] | OOA Folding | |