Information on Result #686986
Linear OA(8172, 32854, F8, 34) (dual of [32854, 32682, 35]-code), using construction X applied to Ce(33) ⊂ Ce(19) based on
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(886, 32768, F8, 20) (dual of [32768, 32682, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(826, 86, F8, 13) (dual of [86, 60, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(826, 130, F8, 13) (dual of [130, 104, 14]-code), using
- trace code [i] based on linear OA(6413, 65, F64, 13) (dual of [65, 52, 14]-code or 65-arc in PG(12,64)), using
- extended Reed–Solomon code RSe(52,64) [i]
- the expurgated narrow-sense BCH-code C(I) with length 65 | 642−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- trace code [i] based on linear OA(6413, 65, F64, 13) (dual of [65, 52, 14]-code or 65-arc in PG(12,64)), using
- discarding factors / shortening the dual code based on linear OA(826, 130, F8, 13) (dual of [130, 104, 14]-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(8173, 32855, F8, 34) (dual of [32855, 32682, 35]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8172, 16427, F8, 2, 34) (dual of [(16427, 2), 32682, 35]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8172, 10951, F8, 3, 34) (dual of [(10951, 3), 32681, 35]-NRT-code) | [i] | ||