Information on Result #686255
Linear OA(8170, 2097167, F8, 28) (dual of [2097167, 2096997, 29]-code), using construction X applied to Ce(27) ⊂ Ce(25) based on
- linear OA(8169, 2097152, F8, 28) (dual of [2097152, 2096983, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-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 | Linear OOA(8170, 1117568, F8, 2, 28) (dual of [(1117568, 2), 2234966, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8170, 1117568, F8, 3, 28) (dual of [(1117568, 3), 3352534, 29]-NRT-code) | [i] | ||
| 3 | Digital (142, 170, 1117568)-net over F8 | [i] | ||
| 4 | Linear OOA(8170, 1048583, F8, 2, 28) (dual of [(1048583, 2), 2096996, 29]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8170, 699055, F8, 3, 28) (dual of [(699055, 3), 2096995, 29]-NRT-code) | [i] | ||