Information on Result #1051712
Linear OOA(2116, 16389, F2, 4, 15) (dual of [(16389, 4), 65440, 16]-NRT-code), using OOA 4-folding based on linear OA(2116, 65556, F2, 15) (dual of [65556, 65440, 16]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2114, 65554, F2, 15) (dual of [65554, 65440, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(297, 65536, F2, 13) (dual of [65536, 65439, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(217, 18, F2, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
- dual of repetition code with length 18 [i]
- linear OA(21, 18, F2, 1) (dual of [18, 17, 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 X4 applied to Ce(14) ⊂ Ce(12) [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(2117, 16389, F2, 4, 15) (dual of [(16389, 4), 65439, 16]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2118, 16389, F2, 4, 15) (dual of [(16389, 4), 65438, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(2115, 16388, F2, 4, 14) (dual of [(16388, 4), 65437, 15]-NRT-code) | [i] | Truncation for OOAs | |