Information on Result #686306
Linear OA(8168, 2097186, F8, 27) (dual of [2097186, 2097018, 28]-code), using construction X applied to Ce(26) ⊂ Ce(21) based on
- linear OA(8162, 2097152, F8, 27) (dual of [2097152, 2096990, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(8168, 1567345, F8, 2, 27) (dual of [(1567345, 2), 3134522, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8168, 1567345, F8, 3, 27) (dual of [(1567345, 3), 4701867, 28]-NRT-code) | [i] | ||
| 3 | Digital (141, 168, 1567345)-net over F8 | [i] | ||
| 4 | Linear OOA(8168, 1048593, F8, 2, 27) (dual of [(1048593, 2), 2097018, 28]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8168, 699062, F8, 3, 27) (dual of [(699062, 3), 2097018, 28]-NRT-code) | [i] | ||