Information on Result #1052524
Linear OOA(2165, 16389, F2, 4, 21) (dual of [(16389, 4), 65391, 22]-NRT-code), using OOA 4-folding based on linear OA(2165, 65556, F2, 21) (dual of [65556, 65391, 22]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2162, 65553, F2, 21) (dual of [65553, 65391, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(2161, 65536, F2, 21) (dual of [65536, 65375, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2145, 65536, F2, 19) (dual of [65536, 65391, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 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
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
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(2165, 16389, F2, 4, 20) (dual of [(16389, 4), 65391, 21]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2166, 16389, F2, 4, 21) (dual of [(16389, 4), 65390, 22]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2164, 16388, F2, 4, 20) (dual of [(16388, 4), 65388, 21]-NRT-code) | [i] | Truncation for OOAs | |