Information on Result #698143
Linear OA(4937, 117664, F49, 12) (dual of [117664, 117627, 13]-code), using construction X applied to Ce(11) ⊂ Ce(7) 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(4922, 117649, F49, 8) (dual of [117649, 117627, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(493, 15, F49, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,49) or 15-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(4937, 114663, F49, 2, 12) (dual of [(114663, 2), 229289, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4937, 114663, F49, 3, 12) (dual of [(114663, 3), 343952, 13]-NRT-code) | [i] | ||
| 3 | Digital (25, 37, 114663)-net over F49 | [i] | ||
| 4 | Linear OOA(4937, 58832, F49, 2, 12) (dual of [(58832, 2), 117627, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4937, 39221, F49, 3, 12) (dual of [(39221, 3), 117626, 13]-NRT-code) | [i] | ||