Information on Result #686200
Linear OA(830, 2097169, F8, 5) (dual of [2097169, 2097139, 6]-code), using construction X4 applied to C([0,2]) ⊂ C([0,1]) based on
- linear OA(829, 2097153, F8, 5) (dual of [2097153, 2097124, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(815, 2097153, F8, 3) (dual of [2097153, 2097138, 4]-code or 2097153-cap in PG(14,8)), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(815, 16, F8, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,8)), using
- dual of repetition code with length 16 [i]
- linear OA(81, 16, F8, 1) (dual of [16, 15, 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(831, 2097170, F8, 5) (dual of [2097170, 2097139, 6]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(830, 2097169, F8, 2, 5) (dual of [(2097169, 2), 4194308, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(830, 2097169, F8, 3, 5) (dual of [(2097169, 3), 6291477, 6]-NRT-code) | [i] | ||
| 4 | Digital (25, 30, 2097169)-net over F8 | [i] | ||
| 5 | Linear OOA(830, 1048584, F8, 3, 5) (dual of [(1048584, 3), 3145722, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 6 | Linear OOA(830, 1048584, F8, 5, 5) (dual of [(1048584, 5), 5242890, 6]-NRT-code) | [i] | ||