Information on Result #687057
Linear OA(866, 4106, F8, 19) (dual of [4106, 4040, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,8]) based on
- linear OA(865, 4097, F8, 19) (dual of [4097, 4032, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(857, 4097, F8, 17) (dual of [4097, 4040, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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(867, 4107, F8, 19) (dual of [4107, 4040, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(868, 4108, F8, 19) (dual of [4108, 4040, 20]-code) | [i] | ||
| 3 | Linear OOA(866, 2900, F8, 2, 19) (dual of [(2900, 2), 5734, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(866, 2900, F8, 3, 19) (dual of [(2900, 3), 8634, 20]-NRT-code) | [i] | ||
| 5 | Digital (47, 66, 2900)-net over F8 | [i] | ||
| 6 | Linear OA(868, 4113, F8, 19) (dual of [4113, 4045, 20]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(869, 4131, F8, 19) (dual of [4131, 4062, 20]-code) | [i] | ||
| 8 | Linear OA(870, 4180, F8, 19) (dual of [4180, 4110, 20]-code) | [i] | ||
| 9 | Linear OA(871, 4305, F8, 19) (dual of [4305, 4234, 20]-code) | [i] | ||
| 10 | Linear OA(872, 4571, F8, 19) (dual of [4571, 4499, 20]-code) | [i] | ||
| 11 | Linear OA(868, 4109, F8, 19) (dual of [4109, 4041, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 12 | Linear OOA(866, 2053, F8, 2, 19) (dual of [(2053, 2), 4040, 20]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(866, 1368, F8, 3, 19) (dual of [(1368, 3), 4038, 20]-NRT-code) | [i] | ||
| 14 | Linear OOA(866, 456, F8, 19, 19) (dual of [(456, 19), 8598, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |