Information on Result #698131
Linear OA(4939, 117660, F49, 13) (dual of [117660, 117621, 14]-code), using construction X applied to Ce(12) ⊂ Ce(9) based on
- linear OA(4937, 117649, F49, 13) (dual of [117649, 117612, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(4928, 117649, F49, 10) (dual of [117649, 117621, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(492, 11, F49, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), 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, 70567, F49, 2, 13) (dual of [(70567, 2), 141095, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4939, 70567, F49, 3, 13) (dual of [(70567, 3), 211662, 14]-NRT-code) | [i] | ||
| 3 | Digital (26, 39, 70567)-net over F49 | [i] | ||
| 4 | Linear OOA(4939, 58830, F49, 2, 13) (dual of [(58830, 2), 117621, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4939, 39220, F49, 3, 13) (dual of [(39220, 3), 117621, 14]-NRT-code) | [i] | ||