Information on Result #686313
Linear OA(8112, 2097186, F8, 18) (dual of [2097186, 2097074, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) based on
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(878, 2097152, F8, 13) (dual of [2097152, 2097074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(86, 34, F8, 4) (dual of [34, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), 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 OOA(8112, 1789061, F8, 2, 18) (dual of [(1789061, 2), 3578010, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8112, 1789061, F8, 3, 18) (dual of [(1789061, 3), 5367071, 19]-NRT-code) | [i] | ||
| 3 | Digital (94, 112, 1789061)-net over F8 | [i] | ||
| 4 | Linear OOA(8112, 1048593, F8, 2, 18) (dual of [(1048593, 2), 2097074, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8112, 699062, F8, 3, 18) (dual of [(699062, 3), 2097074, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(8112, 233020, F8, 18, 18) (dual of [(233020, 18), 4194248, 19]-NRT-code) | [i] | OA Folding and Stacking | |