Information on Result #686609
Linear OA(8108, 262168, F8, 20) (dual of [262168, 262060, 21]-code), using construction XX applied to Ce(19) ⊂ Ce(16) ⊂ Ce(14) based on
- linear OA(8103, 262144, F8, 20) (dual of [262144, 262041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(885, 262144, F8, 17) (dual of [262144, 262059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(879, 262144, F8, 15) (dual of [262144, 262065, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(83, 22, F8, 2) (dual of [22, 19, 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
- linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(8108, 251989, F8, 2, 20) (dual of [(251989, 2), 503870, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8108, 251989, F8, 3, 20) (dual of [(251989, 3), 755859, 21]-NRT-code) | [i] | ||
| 3 | Digital (88, 108, 251989)-net over F8 | [i] | ||
| 4 | Linear OOA(8108, 131084, F8, 2, 20) (dual of [(131084, 2), 262060, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8108, 87389, F8, 3, 20) (dual of [(87389, 3), 262059, 21]-NRT-code) | [i] | ||