Information on Result #686413
Linear OA(898, 262158, F8, 19) (dual of [262158, 262060, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,8]) based on
- linear OA(897, 262145, F8, 19) (dual of [262145, 262048, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(81, 13, F8, 1) (dual of [13, 12, 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(899, 262159, F8, 19) (dual of [262159, 262060, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8100, 262160, F8, 19) (dual of [262160, 262060, 20]-code) | [i] | ||
| 3 | Linear OOA(898, 145795, F8, 2, 19) (dual of [(145795, 2), 291492, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(898, 145795, F8, 3, 19) (dual of [(145795, 3), 437287, 20]-NRT-code) | [i] | ||
| 5 | Digital (79, 98, 145795)-net over F8 | [i] | ||
| 6 | Linear OA(8100, 262161, F8, 19) (dual of [262161, 262061, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(898, 131079, F8, 2, 19) (dual of [(131079, 2), 262060, 20]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(898, 87386, F8, 3, 19) (dual of [(87386, 3), 262060, 20]-NRT-code) | [i] | ||
| 9 | Linear OOA(898, 29128, F8, 19, 19) (dual of [(29128, 19), 553334, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |