Information on Result #686803
Linear OA(8169, 32786, F8, 38) (dual of [32786, 32617, 39]-code), using construction X applied to Ce(37) ⊂ Ce(34) based on
- linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(8151, 32768, F8, 35) (dual of [32768, 32617, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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 OOA(8169, 32786, F8, 2, 38) (dual of [(32786, 2), 65403, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8169, 32786, F8, 3, 38) (dual of [(32786, 3), 98189, 39]-NRT-code) | [i] | ||
| 3 | Digital (131, 169, 32786)-net over F8 | [i] | ||
| 4 | Linear OOA(8169, 16393, F8, 2, 38) (dual of [(16393, 2), 32617, 39]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8169, 10928, F8, 3, 38) (dual of [(10928, 3), 32615, 39]-NRT-code) | [i] | ||