Information on Result #699134
Linear OA(8166, 531465, F81, 21) (dual of [531465, 531399, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,7]) based on
- linear OA(8161, 531442, F81, 21) (dual of [531442, 531381, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(8143, 531442, F81, 15) (dual of [531442, 531399, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(815, 23, F81, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,81)), using
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- Reed–Solomon code RS(76,81) [i]
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), 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(8166, 335075, F81, 2, 21) (dual of [(335075, 2), 670084, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8166, 335075, F81, 3, 21) (dual of [(335075, 3), 1005159, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(8166, 335075, F81, 4, 21) (dual of [(335075, 4), 1340234, 22]-NRT-code) | [i] | ||
| 4 | Digital (45, 66, 335075)-net over F81 | [i] | ||
| 5 | Linear OOA(8166, 265732, F81, 2, 21) (dual of [(265732, 2), 531398, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8166, 177155, F81, 3, 21) (dual of [(177155, 3), 531399, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(8166, 132866, F81, 4, 21) (dual of [(132866, 4), 531398, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(8166, 53146, F81, 21, 21) (dual of [(53146, 21), 1116000, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |