Information on Result #1462117
Linear OOA(4928, 117665, F49, 2, 9) (dual of [(117665, 2), 235302, 10]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4928, 117665, F49, 9) (dual of [117665, 117637, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,2]) [i] based on
- linear OA(4925, 117650, F49, 9) (dual of [117650, 117625, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(4913, 117650, F49, 5) (dual of [117650, 117637, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [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: 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(4928, 58832, F49, 3, 9) (dual of [(58832, 3), 176468, 10]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4928, 58832, F49, 10, 9) (dual of [(58832, 10), 588292, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |