Information on Result #699737
Linear OA(12811, 2097160, F128, 4) (dual of [2097160, 2097149, 5]-code), using construction X4 applied to Ce(3) ⊂ Ce(1) based on
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1284, 2097152, F128, 2) (dual of [2097152, 2097148, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(1287, 8, F128, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,128)), using
- dual of repetition code with length 8 [i]
- linear OA(1281, 8, F128, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, 128, F128, 1) (dual of [128, 127, 2]-code), using
- Reed–Solomon code RS(127,128) [i]
- discarding factors / shortening the dual code based on linear OA(1281, 128, F128, 1) (dual of [128, 127, 2]-code), using
Mode: Constructive and 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(12811, 2097160, F128, 2, 4) (dual of [(2097160, 2), 4194309, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12811, 2097160, F128, 3, 4) (dual of [(2097160, 3), 6291469, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(12811, 1048580, F128, 2, 4) (dual of [(1048580, 2), 2097149, 5]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(12811, 1048580, F128, 3, 4) (dual of [(1048580, 3), 3145729, 5]-NRT-code) | [i] | OA Folding and Stacking | |
| 5 | Linear OOA(12811, 1048580, F128, 4, 4) (dual of [(1048580, 4), 4194309, 5]-NRT-code) | [i] | ||