Information on Result #698140
Linear OA(4955, 117664, F49, 18) (dual of [117664, 117609, 19]-code), using construction X applied to Ce(17) ⊂ Ce(13) based on
- linear OA(4952, 117649, F49, 18) (dual of [117649, 117597, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(4940, 117649, F49, 14) (dual of [117649, 117609, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(4955, 71724, F49, 2, 18) (dual of [(71724, 2), 143393, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4955, 71724, F49, 3, 18) (dual of [(71724, 3), 215117, 19]-NRT-code) | [i] | ||
| 3 | Digital (37, 55, 71724)-net over F49 | [i] | ||
| 4 | Linear OOA(4955, 58832, F49, 2, 18) (dual of [(58832, 2), 117609, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4955, 39221, F49, 3, 18) (dual of [(39221, 3), 117608, 19]-NRT-code) | [i] | ||