Information on Result #687162
Linear OA(8142, 4101, F8, 41) (dual of [4101, 3959, 42]-code), using construction X applied to Ce(40) ⊂ Ce(38) based on
- linear OA(8141, 4096, F8, 41) (dual of [4096, 3955, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(8137, 4096, F8, 39) (dual of [4096, 3959, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(81, 5, F8, 1) (dual of [5, 4, 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(8141, 4100, F8, 40) (dual of [4100, 3959, 41]-code) | [i] | Truncation | |
| 2 | Linear OOA(8142, 4025, F8, 2, 41) (dual of [(4025, 2), 7908, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8142, 4025, F8, 3, 41) (dual of [(4025, 3), 11933, 42]-NRT-code) | [i] | ||
| 4 | Digital (101, 142, 4025)-net over F8 | [i] | ||
| 5 | Linear OA(8143, 4107, F8, 41) (dual of [4107, 3964, 42]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OOA(8142, 2050, F8, 2, 41) (dual of [(2050, 2), 3958, 42]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(8142, 1367, F8, 3, 41) (dual of [(1367, 3), 3959, 42]-NRT-code) | [i] | ||