Information on Result #1323808
Linear OA(8137, 2097204, F8, 21) (dual of [2097204, 2097067, 22]-code), using construction X applied to Ce(20) ⊂ Ce(13) based on
- linear OA(8127, 2097152, F8, 21) (dual of [2097152, 2097025, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(810, 52, F8, 6) (dual of [52, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
Mode: 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(8137, 2097204, F8, 2, 21) (dual of [(2097204, 2), 4194271, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8137, 2097204, F8, 3, 21) (dual of [(2097204, 3), 6291475, 22]-NRT-code) | [i] | ||
| 3 | Digital (116, 137, 2097204)-net over F8 | [i] | ||
| 4 | Linear OA(8138, 2097206, F8, 21) (dual of [2097206, 2097068, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(8137, 1048602, F8, 2, 21) (dual of [(1048602, 2), 2097067, 22]-NRT-code) | [i] | OOA Folding | |