Information on Result #1566512
Linear OOA(12835, 1048579, F128, 3, 12) (dual of [(1048579, 3), 3145702, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12835, 1048579, F128, 2, 12) (dual of [(1048579, 2), 2097123, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12835, 2097158, F128, 12) (dual of [2097158, 2097123, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12835, 2097159, F128, 12) (dual of [2097159, 2097124, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [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(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 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(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(12835, 2097159, F128, 12) (dual of [2097159, 2097124, 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(6441, 1048579, S64, 3, 12) | [i] | Discarding Parts of the Base for OOAs | |
| 2 | Linear OOA(12835, 524289, F128, 15, 12) (dual of [(524289, 15), 7864300, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |