Information on Result #698272
Linear OA(4934, 2412, F49, 16) (dual of [2412, 2378, 17]-code), using construction X applied to Ce(15) ⊂ Ce(11) based on
- linear OA(4931, 2401, F49, 16) (dual of [2401, 2370, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(4934, 1208, F49, 2, 16) (dual of [(1208, 2), 2382, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4934, 1208, F49, 3, 16) (dual of [(1208, 3), 3590, 17]-NRT-code) | [i] | ||
| 3 | Digital (18, 34, 1208)-net over F49 | [i] | ||
| 4 | Linear OOA(4934, 1206, F49, 2, 16) (dual of [(1206, 2), 2378, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4934, 804, F49, 3, 16) (dual of [(804, 3), 2378, 17]-NRT-code) | [i] | ||