Information on Result #686625
Linear OA(8162, 32780, F8, 37) (dual of [32780, 32618, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,17]) based on
- 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(8151, 32769, F8, 35) (dual of [32769, 32618, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (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(8163, 32781, F8, 37) (dual of [32781, 32618, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8162, 28317, F8, 2, 37) (dual of [(28317, 2), 56472, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8162, 28317, F8, 3, 37) (dual of [(28317, 3), 84789, 38]-NRT-code) | [i] | ||
| 4 | Digital (125, 162, 28317)-net over F8 | [i] | ||
| 5 | Linear OOA(8162, 16390, F8, 2, 37) (dual of [(16390, 2), 32618, 38]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8162, 10926, F8, 3, 37) (dual of [(10926, 3), 32616, 38]-NRT-code) | [i] | ||
| 7 | Linear OOA(8162, 1821, F8, 37, 37) (dual of [(1821, 37), 67215, 38]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |