Information on Result #699358
Linear OA(8150, 6591, F81, 21) (dual of [6591, 6541, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,5]) based on
- linear OA(8141, 6562, F81, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(8121, 6562, F81, 11) (dual of [6562, 6541, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(819, 29, F81, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,81)), using
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), using
- Reed–Solomon code RS(72,81) [i]
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), 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(8150, 6591, F81, 2, 21) (dual of [(6591, 2), 13132, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8150, 6591, F81, 3, 21) (dual of [(6591, 3), 19723, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(8150, 6591, F81, 4, 21) (dual of [(6591, 4), 26314, 22]-NRT-code) | [i] | ||
| 4 | Digital (29, 50, 6591)-net over F81 | [i] | ||
| 5 | Linear OOA(8150, 3295, F81, 2, 21) (dual of [(3295, 2), 6540, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8150, 2197, F81, 3, 21) (dual of [(2197, 3), 6541, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(8150, 1647, F81, 4, 21) (dual of [(1647, 4), 6538, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(8150, 659, F81, 21, 21) (dual of [(659, 21), 13789, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |