Information on Result #698071
Linear OA(4950, 5764830, F49, 12) (dual of [5764830, 5764780, 13]-code), using construction X applied to Ce(11) ⊂ Ce(5) based on
- linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(495, 29, F49, 5) (dual of [29, 24, 6]-code or 29-arc in PG(4,49)), using
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), using
- Reed–Solomon code RS(44,49) [i]
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), 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(4950, 5764830, F49, 2, 12) (dual of [(5764830, 2), 11529610, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4950, 5764830, F49, 3, 12) (dual of [(5764830, 3), 17294440, 13]-NRT-code) | [i] | ||
| 3 | Digital (38, 50, 5764830)-net over F49 | [i] | ||
| 4 | Linear OOA(4950, 2882415, F49, 2, 12) (dual of [(2882415, 2), 5764780, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4950, 1921610, F49, 3, 12) (dual of [(1921610, 3), 5764780, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(4950, 960805, F49, 12, 12) (dual of [(960805, 12), 11529610, 13]-NRT-code) | [i] | OA Folding and Stacking | |