Information on Result #687044
Linear OA(8130, 4106, F8, 37) (dual of [4106, 3976, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,17]) based on
- 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(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(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(8131, 4107, F8, 37) (dual of [4107, 3976, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8130, 4106, F8, 2, 37) (dual of [(4106, 2), 8082, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8130, 4106, F8, 3, 37) (dual of [(4106, 3), 12188, 38]-NRT-code) | [i] | ||
| 4 | Digital (93, 130, 4106)-net over F8 | [i] | ||
| 5 | Linear OA(8131, 4131, F8, 37) (dual of [4131, 4000, 38]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(8132, 4239, F8, 37) (dual of [4239, 4107, 38]-code) | [i] | ||
| 7 | Linear OA(8131, 4108, F8, 37) (dual of [4108, 3977, 38]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OOA(8130, 2053, F8, 2, 37) (dual of [(2053, 2), 3976, 38]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(8130, 1368, F8, 3, 37) (dual of [(1368, 3), 3974, 38]-NRT-code) | [i] | ||