Information on Result #841228
Linear OOA(7110, 58828, F7, 2, 22) (dual of [(58828, 2), 117546, 23]-NRT-code), using OOA 2-folding based on linear OA(7110, 117656, F7, 22) (dual of [117656, 117546, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(7109, 117649, F7, 22) (dual of [117649, 117540, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(7103, 117649, F7, 20) (dual of [117649, 117546, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 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 OOA(7110, 58828, F7, 3, 22) (dual of [(58828, 3), 176374, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (88, 110, 58828)-net over F7 | [i] | ||