Information on Result #686796
Linear OA(839, 32781, F8, 9) (dual of [32781, 32742, 10]-code), using construction X applied to Ce(8) ⊂ Ce(5) based on
- 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(826, 32768, F8, 6) (dual of [32768, 32742, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(83, 13, F8, 2) (dual of [13, 10, 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(839, 32781, F8, 2, 9) (dual of [(32781, 2), 65523, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(839, 32781, F8, 3, 9) (dual of [(32781, 3), 98304, 10]-NRT-code) | [i] | ||
| 3 | Digital (30, 39, 32781)-net over F8 | [i] | ||
| 4 | Linear OOA(839, 16390, F8, 2, 9) (dual of [(16390, 2), 32741, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(839, 10927, F8, 3, 9) (dual of [(10927, 3), 32742, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(839, 8195, F8, 9, 9) (dual of [(8195, 9), 73716, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |