Information on Result #1566502
Linear OOA(12834, 1014491, F128, 3, 12) (dual of [(1014491, 3), 3043439, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12834, 1014491, F128, 2, 12) (dual of [(1014491, 2), 2028948, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12834, 1048577, F128, 2, 12) (dual of [(1048577, 2), 2097120, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12834, 2097154, F128, 12) (dual of [2097154, 2097120, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12834, 2097155, F128, 12) (dual of [2097155, 2097121, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(12834, 2097155, F128, 12) (dual of [2097155, 2097121, 13]-code), using
- OOA 2-folding [i] based on linear OA(12834, 2097154, F128, 12) (dual of [2097154, 2097120, 13]-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 | OOA(6440, 1014491, S64, 3, 12) | [i] | Discarding Parts of the Base for OOAs | |
| 2 | Linear OOA(12834, 507245, F128, 15, 12) (dual of [(507245, 15), 7608641, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |