Information on Result #686646
Linear OA(832, 32781, F8, 7) (dual of [32781, 32749, 8]-code), using construction X4 applied to C([0,3]) ⊂ C([0,2]) based on
- linear OA(831, 32769, F8, 7) (dual of [32769, 32738, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(821, 32769, F8, 5) (dual of [32769, 32748, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(811, 12, F8, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,8)), using
- dual of repetition code with length 12 [i]
- linear OA(81, 12, F8, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-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(833, 32782, F8, 7) (dual of [32782, 32749, 8]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(832, 32781, F8, 2, 7) (dual of [(32781, 2), 65530, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(832, 32781, F8, 3, 7) (dual of [(32781, 3), 98311, 8]-NRT-code) | [i] | ||
| 4 | Digital (25, 32, 32781)-net over F8 | [i] | ||
| 5 | Linear OOA(832, 10927, F8, 3, 7) (dual of [(10927, 3), 32749, 8]-NRT-code) | [i] | OOA Folding | |