Information on Result #686323
Linear OA(8169, 2097194, F8, 27) (dual of [2097194, 2097025, 28]-code), using construction X applied to Ce(26) ⊂ Ce(20) based on
- linear OA(8162, 2097152, F8, 27) (dual of [2097152, 2096990, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8127, 2097152, F8, 21) (dual of [2097152, 2097025, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(87, 42, F8, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-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 OA(8170, 2097195, F8, 27) (dual of [2097195, 2097025, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8171, 2097196, F8, 27) (dual of [2097196, 2097025, 28]-code) | [i] | ||
| 3 | Linear OA(8172, 2097197, F8, 27) (dual of [2097197, 2097025, 28]-code) | [i] | ||
| 4 | Linear OA(8171, 2097197, F8, 27) (dual of [2097197, 2097026, 28]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(8172, 2097199, F8, 27) (dual of [2097199, 2097027, 28]-code) | [i] | ||
| 6 | Linear OOA(8169, 1048597, F8, 2, 27) (dual of [(1048597, 2), 2097025, 28]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(8169, 699064, F8, 3, 27) (dual of [(699064, 3), 2097023, 28]-NRT-code) | [i] | ||
| 8 | Linear OOA(8169, 161322, F8, 27, 27) (dual of [(161322, 27), 4355525, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |