Information on Result #684603
Linear OA(7110, 117663, F7, 21) (dual of [117663, 117553, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,9]) based on
- linear OA(7109, 117650, F7, 21) (dual of [117650, 117541, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 712−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(797, 117650, F7, 19) (dual of [117650, 117553, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 712−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(71, 13, F7, 1) (dual of [13, 12, 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, 93155, F7, 2, 21) (dual of [(93155, 2), 186200, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(7110, 93155, F7, 3, 21) (dual of [(93155, 3), 279355, 22]-NRT-code) | [i] | ||
| 3 | Digital (89, 110, 93155)-net over F7 | [i] | ||
| 4 | Linear OOA(7110, 58831, F7, 2, 21) (dual of [(58831, 2), 117552, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(7110, 39221, F7, 3, 21) (dual of [(39221, 3), 117553, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(7110, 11766, F7, 21, 21) (dual of [(11766, 21), 246976, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |