Information on Result #699304
Linear OA(8130, 6567, F81, 15) (dual of [6567, 6537, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,6]) based on
- linear OA(8129, 6562, F81, 15) (dual of [6562, 6533, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(8125, 6562, F81, 13) (dual of [6562, 6537, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 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 OA(960, 13134, F9, 15) (dual of [13134, 13074, 16]-code) | [i] | Trace Code | |
| 2 | OA(2740, 6567, S27, 15) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(8130, 3283, F81, 2, 15) (dual of [(3283, 2), 6536, 16]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(8130, 2189, F81, 3, 15) (dual of [(2189, 3), 6537, 16]-NRT-code) | [i] | ||
| 5 | Linear OOA(8130, 1641, F81, 4, 15) (dual of [(1641, 4), 6534, 16]-NRT-code) | [i] | ||
| 6 | Linear OOA(8130, 938, F81, 15, 15) (dual of [(938, 15), 14040, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |