Information on Result #698156
Linear OA(4939, 117672, F49, 12) (dual of [117672, 117633, 13]-code), using construction X applied to Ce(11) ⊂ Ce(5) based on
- linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4916, 117649, F49, 6) (dual of [117649, 117633, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(495, 23, F49, 5) (dual of [23, 18, 6]-code or 23-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(4939, 117672, F49, 2, 12) (dual of [(117672, 2), 235305, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4939, 117672, F49, 3, 12) (dual of [(117672, 3), 352977, 13]-NRT-code) | [i] | ||
| 3 | Digital (27, 39, 117672)-net over F49 | [i] | ||
| 4 | Linear OOA(4939, 58836, F49, 2, 12) (dual of [(58836, 2), 117633, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4939, 39224, F49, 3, 12) (dual of [(39224, 3), 117633, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(4939, 19612, F49, 12, 12) (dual of [(19612, 12), 235305, 13]-NRT-code) | [i] | OA Folding and Stacking | |