Information on Result #698181
Linear OA(4924, 2413, F49, 11) (dual of [2413, 2389, 12]-code), using construction X applied to C([0,5]) ⊂ C([0,3]) based on
- linear OA(4921, 2402, F49, 11) (dual of [2402, 2381, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(4913, 2402, F49, 7) (dual of [2402, 2389, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(493, 11, F49, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,49) or 11-cap in PG(2,49)), using
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- Reed–Solomon code RS(46,49) [i]
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), 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(4924, 1799, F49, 2, 11) (dual of [(1799, 2), 3574, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4924, 1799, F49, 3, 11) (dual of [(1799, 3), 5373, 12]-NRT-code) | [i] | ||
| 3 | Digital (13, 24, 1799)-net over F49 | [i] | ||
| 4 | Linear OOA(4924, 1206, F49, 2, 11) (dual of [(1206, 2), 2388, 12]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4924, 804, F49, 3, 11) (dual of [(804, 3), 2388, 12]-NRT-code) | [i] | ||
| 6 | Linear OOA(4924, 482, F49, 11, 11) (dual of [(482, 11), 5278, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |