Information on Result #686624
Linear OA(8172, 32780, F8, 39) (dual of [32780, 32608, 40]-code), using construction X applied to C([0,19]) ⊂ C([0,18]) based on
- linear OA(8171, 32769, F8, 39) (dual of [32769, 32598, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(8161, 32769, F8, 37) (dual of [32769, 32608, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 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(8173, 32781, F8, 39) (dual of [32781, 32608, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8172, 31206, F8, 2, 39) (dual of [(31206, 2), 62240, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8172, 31206, F8, 3, 39) (dual of [(31206, 3), 93446, 40]-NRT-code) | [i] | ||
| 4 | Digital (133, 172, 31206)-net over F8 | [i] | ||
| 5 | Linear OA(8173, 32782, F8, 39) (dual of [32782, 32609, 40]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(8172, 16390, F8, 2, 39) (dual of [(16390, 2), 32608, 40]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(8172, 10926, F8, 3, 39) (dual of [(10926, 3), 32606, 40]-NRT-code) | [i] | ||
| 8 | Linear OOA(8172, 1725, F8, 39, 39) (dual of [(1725, 39), 67103, 40]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |