Information on Result #688713
Linear OA(8106, 178, F8, 51) (dual of [178, 72, 52]-code), using construction X applied to C([0,25]) ⊂ C([0,24]) based on
- linear OA(8105, 171, F8, 51) (dual of [171, 66, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 171 | 86−1, defining interval I = [0,25], and minimum distance d ≥ |{−25,−24,…,25}|+1 = 52 (BCH-bound) [i]
- linear OA(899, 171, F8, 49) (dual of [171, 72, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 171 | 86−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- linear OA(81, 7, F8, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 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(8107, 179, F8, 51) (dual of [179, 72, 52]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8105, 177, F8, 50) (dual of [177, 72, 51]-code) | [i] | Truncation | |
| 3 | Linear OOA(8106, 89, F8, 2, 51) (dual of [(89, 2), 72, 52]-NRT-code) | [i] | OOA Folding | |