Information on Result #2221886
Linear OA(285, 16399, F2, 12) (dual of [16399, 16314, 13]-code), using 1 times truncation based on linear OA(286, 16400, F2, 13) (dual of [16400, 16314, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(285, 16384, F2, 13) (dual of [16384, 16299, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(271, 16384, F2, 11) (dual of [16384, 16313, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(215, 16, F2, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
- dual of repetition code with length 16 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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 OA(287, 16401, F2, 12) (dual of [16401, 16314, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(288, 16402, F2, 12) (dual of [16402, 16314, 13]-code) | [i] | ||
| 3 | Linear OA(289, 16403, F2, 12) (dual of [16403, 16314, 13]-code) | [i] | ||
| 4 | Linear OOA(285, 8199, F2, 2, 12) (dual of [(8199, 2), 16313, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(285, 5466, F2, 3, 12) (dual of [(5466, 3), 16313, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(285, 4099, F2, 4, 12) (dual of [(4099, 4), 16311, 13]-NRT-code) | [i] | ||
| 7 | Linear OOA(285, 3279, F2, 5, 12) (dual of [(3279, 5), 16310, 13]-NRT-code) | [i] | ||
| 8 | Linear OOA(285, 2733, F2, 6, 12) (dual of [(2733, 6), 16313, 13]-NRT-code) | [i] | ||
| 9 | Linear OOA(285, 2733, F2, 7, 12) (dual of [(2733, 7), 19046, 13]-NRT-code) | [i] | OA Folding and Stacking | |
| 10 | Linear OOA(285, 2733, F2, 8, 12) (dual of [(2733, 8), 21779, 13]-NRT-code) | [i] | ||
| 11 | Linear OOA(285, 2733, F2, 12, 12) (dual of [(2733, 12), 32711, 13]-NRT-code) | [i] | ||