Information on Result #699721
Linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) 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(1287, 2097152, F128, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(1618, 2097155, S16, 4) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3214, 2097155, S32, 4) | [i] | ||
| 3 | OA(6412, 2097155, S64, 4) | [i] | ||
| 4 | Linear OOA(12810, 2097155, F128, 2, 4) (dual of [(2097155, 2), 4194300, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(12810, 2097155, F128, 3, 4) (dual of [(2097155, 3), 6291455, 5]-NRT-code) | [i] | ||
| 6 | Linear OOA(12810, 1048577, F128, 2, 4) (dual of [(1048577, 2), 2097144, 5]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12810, 1048577, F128, 3, 4) (dual of [(1048577, 3), 3145721, 5]-NRT-code) | [i] | OA Folding and Stacking | |
| 8 | Linear OOA(12810, 1048577, F128, 4, 4) (dual of [(1048577, 4), 4194298, 5]-NRT-code) | [i] | ||