Information on Result #699720
Linear OA(12813, 2097155, F128, 5) (dual of [2097155, 2097142, 6]-code), using construction X applied to Ce(4) ⊂ Ce(3) based on
- linear OA(12813, 2097152, F128, 5) (dual of [2097152, 2097139, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- 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(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
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 | OA(1623, 2097155, S16, 5) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3219, 2097155, S32, 5) | [i] | ||
| 3 | OA(6416, 2097155, S64, 5) | [i] | ||
| 4 | Linear OOA(12813, 2097155, F128, 2, 5) (dual of [(2097155, 2), 4194297, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(12813, 2097155, F128, 3, 5) (dual of [(2097155, 3), 6291452, 6]-NRT-code) | [i] | ||
| 6 | Linear OOA(12813, 2097155, F128, 4, 5) (dual of [(2097155, 4), 8388607, 6]-NRT-code) | [i] | ||
| 7 | Linear OOA(12813, 1048577, F128, 2, 5) (dual of [(1048577, 2), 2097141, 6]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(12813, 1048577, F128, 3, 5) (dual of [(1048577, 3), 3145718, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 9 | Linear OOA(12813, 1048577, F128, 4, 5) (dual of [(1048577, 4), 4194295, 6]-NRT-code) | [i] | ||