Information on Result #686875
Linear OA(8113, 32800, F8, 25) (dual of [32800, 32687, 26]-code), using construction X applied to Ce(24) ⊂ Ce(18) based on
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(881, 32768, F8, 19) (dual of [32768, 32687, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-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 OA(8114, 32801, F8, 25) (dual of [32801, 32687, 26]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8115, 32802, F8, 25) (dual of [32802, 32687, 26]-code) | [i] | ||
| 3 | Linear OA(8112, 32799, F8, 24) (dual of [32799, 32687, 25]-code) | [i] | Truncation | |
| 4 | Linear OOA(8113, 32800, F8, 2, 25) (dual of [(32800, 2), 65487, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(8113, 32800, F8, 3, 25) (dual of [(32800, 3), 98287, 26]-NRT-code) | [i] | ||
| 6 | Digital (88, 113, 32800)-net over F8 | [i] | ||
| 7 | Linear OA(8114, 32802, F8, 25) (dual of [32802, 32688, 26]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(8115, 32804, F8, 25) (dual of [32804, 32689, 26]-code) | [i] | ||
| 9 | Linear OOA(8113, 16400, F8, 2, 25) (dual of [(16400, 2), 32687, 26]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(8113, 10933, F8, 3, 25) (dual of [(10933, 3), 32686, 26]-NRT-code) | [i] | ||
| 11 | Linear OOA(8113, 2733, F8, 25, 25) (dual of [(2733, 25), 68212, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |