Information on Result #686257
Linear OA(8158, 2097169, F8, 26) (dual of [2097169, 2097011, 27]-code), using construction X applied to Ce(25) ⊂ Ce(22) based on
- linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8141, 2097152, F8, 23) (dual of [2097152, 2097011, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(83, 17, F8, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-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(8158, 1132330, F8, 2, 26) (dual of [(1132330, 2), 2264502, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8158, 1132330, F8, 3, 26) (dual of [(1132330, 3), 3396832, 27]-NRT-code) | [i] | ||
| 3 | Digital (132, 158, 1132330)-net over F8 | [i] | ||
| 4 | Linear OOA(8158, 1048584, F8, 2, 26) (dual of [(1048584, 2), 2097010, 27]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8158, 699056, F8, 3, 26) (dual of [(699056, 3), 2097010, 27]-NRT-code) | [i] | ||