Information on Result #698147
Linear OA(4950, 117668, F49, 16) (dual of [117668, 117618, 17]-code), using construction X applied to Ce(15) ⊂ Ce(10) based on
- linear OA(4946, 117649, F49, 16) (dual of [117649, 117603, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(4931, 117649, F49, 11) (dual of [117649, 117618, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(494, 19, F49, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,49)), using
- discarding factors / shortening the dual code based on linear OA(494, 49, F49, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), using
- Reed–Solomon code RS(45,49) [i]
- discarding factors / shortening the dual code based on linear OA(494, 49, F49, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), 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, 103723, F49, 2, 16) (dual of [(103723, 2), 207396, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4950, 103723, F49, 3, 16) (dual of [(103723, 3), 311119, 17]-NRT-code) | [i] | ||
| 3 | Digital (34, 50, 103723)-net over F49 | [i] | ||
| 4 | Linear OOA(4950, 58834, F49, 2, 16) (dual of [(58834, 2), 117618, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4950, 39222, F49, 3, 16) (dual of [(39222, 3), 117616, 17]-NRT-code) | [i] | ||