Information on Result #672178
Linear OA(2178, 4194327, F2, 17) (dual of [4194327, 4194149, 18]-code), using construction X applied to Ce(16) ⊂ Ce(14) based on
- linear OA(2177, 4194304, F2, 17) (dual of [4194304, 4194127, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2155, 4194304, F2, 15) (dual of [4194304, 4194149, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 23, F2, 1) (dual of [23, 22, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 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(2178, 1398109, F2, 3, 17) (dual of [(1398109, 3), 4194149, 18]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2178, 838865, F2, 5, 17) (dual of [(838865, 5), 4194147, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(2178, 699054, F2, 6, 17) (dual of [(699054, 6), 4194146, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(2178, 599189, F2, 7, 17) (dual of [(599189, 7), 4194145, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(2178, 524290, F2, 17, 17) (dual of [(524290, 17), 8912752, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |