Information on Result #1441197
Linear OOA(757, 5066, F7, 2, 14) (dual of [(5066, 2), 10075, 15]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(757, 5066, F7, 14) (dual of [5066, 5009, 15]-code), using
- 257 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 40 times 0, 1, 209 times 0) [i] based on linear OA(754, 4806, F7, 14) (dual of [4806, 4752, 15]-code), using
- trace code [i] based on linear OA(4927, 2403, F49, 14) (dual of [2403, 2376, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(4927, 2401, F49, 14) (dual of [2401, 2374, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(4925, 2401, F49, 13) (dual of [2401, 2376, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- trace code [i] based on linear OA(4927, 2403, F49, 14) (dual of [2403, 2376, 15]-code), 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(757, 2533, F7, 3, 14) (dual of [(2533, 3), 7542, 15]-NRT-code) | [i] | OOA Folding | |