Information on Result #1614287
Linear OOA(12816, 8194, F128, 4, 8) (dual of [(8194, 4), 32760, 9]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12816, 8194, F128, 2, 8) (dual of [(8194, 2), 16372, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12816, 16388, F128, 8) (dual of [16388, 16372, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(12816, 16389, F128, 8) (dual of [16389, 16373, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(12815, 16384, F128, 8) (dual of [16384, 16369, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(12811, 16384, F128, 6) (dual of [16384, 16373, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(12816, 16389, F128, 8) (dual of [16389, 16373, 9]-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(12816, 8193, F128, 12, 8) (dual of [(8193, 12), 98300, 9]-NRT-code) | [i] | OOA Stacking with Additional Row | |