Information on Result #687043
Linear OA(8138, 4106, F8, 39) (dual of [4106, 3968, 40]-code), using construction X applied to C([0,19]) ⊂ C([0,18]) based on
- linear OA(8137, 4097, F8, 39) (dual of [4097, 3960, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(8129, 4097, F8, 37) (dual of [4097, 3968, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(81, 9, F8, 1) (dual of [9, 8, 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(8139, 4107, F8, 39) (dual of [4107, 3968, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8138, 2053, F8, 2, 39) (dual of [(2053, 2), 3968, 40]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8138, 1368, F8, 3, 39) (dual of [(1368, 3), 3966, 40]-NRT-code) | [i] | ||