Information on Result #686830
Linear OA(854, 32786, F8, 12) (dual of [32786, 32732, 13]-code), using construction X applied to Ce(11) ⊂ Ce(8) based on
- linear OA(851, 32768, F8, 12) (dual of [32768, 32717, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(83, 18, F8, 2) (dual of [18, 15, 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 OA(855, 32787, F8, 12) (dual of [32787, 32732, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(854, 32786, F8, 2, 12) (dual of [(32786, 2), 65518, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(854, 32786, F8, 3, 12) (dual of [(32786, 3), 98304, 13]-NRT-code) | [i] | ||
| 4 | Digital (42, 54, 32786)-net over F8 | [i] | ||
| 5 | Linear OA(855, 32788, F8, 12) (dual of [32788, 32733, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(856, 32790, F8, 12) (dual of [32790, 32734, 13]-code) | [i] | ||
| 7 | Linear OOA(854, 16393, F8, 2, 12) (dual of [(16393, 2), 32732, 13]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(854, 10928, F8, 3, 12) (dual of [(10928, 3), 32730, 13]-NRT-code) | [i] | ||
| 9 | Linear OOA(854, 5464, F8, 12, 12) (dual of [(5464, 12), 65514, 13]-NRT-code) | [i] | OA Folding and Stacking | |