Information on Result #699316
Linear OA(8152, 6573, F81, 25) (dual of [6573, 6521, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,10]) based on
- linear OA(8149, 6562, F81, 25) (dual of [6562, 6513, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 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(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), 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 OA(9104, 13146, F9, 25) (dual of [13146, 13042, 26]-code) | [i] | Trace Code | |
| 2 | OA(2770, 6573, S27, 25) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(8152, 3286, F81, 2, 25) (dual of [(3286, 2), 6520, 26]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(8152, 2191, F81, 3, 25) (dual of [(2191, 3), 6521, 26]-NRT-code) | [i] | ||
| 5 | Linear OOA(8152, 1643, F81, 4, 25) (dual of [(1643, 4), 6520, 26]-NRT-code) | [i] | ||