Information on Result #687045
Linear OA(8122, 4106, F8, 35) (dual of [4106, 3984, 36]-code), using construction X applied to C([0,17]) ⊂ C([0,16]) based on
- linear OA(8121, 4097, F8, 35) (dual of [4097, 3976, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(8113, 4097, F8, 33) (dual of [4097, 3984, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (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(8123, 4107, F8, 35) (dual of [4107, 3984, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8124, 4108, F8, 35) (dual of [4108, 3984, 36]-code) | [i] | ||
| 3 | Linear OOA(8122, 3831, F8, 2, 35) (dual of [(3831, 2), 7540, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(8122, 3831, F8, 3, 35) (dual of [(3831, 3), 11371, 36]-NRT-code) | [i] | ||
| 5 | Digital (87, 122, 3831)-net over F8 | [i] | ||
| 6 | Linear OA(8123, 4108, F8, 35) (dual of [4108, 3985, 36]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(8124, 4110, F8, 35) (dual of [4110, 3986, 36]-code) | [i] | ||
| 8 | Linear OOA(8122, 2053, F8, 2, 35) (dual of [(2053, 2), 3984, 36]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(8122, 1368, F8, 3, 35) (dual of [(1368, 3), 3982, 36]-NRT-code) | [i] | ||