Information on Result #2222305
Linear OA(291, 32784, F2, 12) (dual of [32784, 32693, 13]-code), using 1 times truncation based on linear OA(292, 32785, F2, 13) (dual of [32785, 32693, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(291, 32768, F2, 13) (dual of [32768, 32677, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(276, 32768, F2, 11) (dual of [32768, 32692, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(216, 17, F2, 15) (dual of [17, 1, 16]-code), using
- strength reduction [i] based on linear OA(216, 17, F2, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
- dual of repetition code with length 17 [i]
- strength reduction [i] based on linear OA(216, 17, F2, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
- 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
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(293, 32786, F2, 12) (dual of [32786, 32693, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(294, 32787, F2, 12) (dual of [32787, 32693, 13]-code) | [i] | ||
| 3 | Linear OA(295, 32788, F2, 12) (dual of [32788, 32693, 13]-code) | [i] | ||
| 4 | Linear OOA(291, 16392, F2, 2, 12) (dual of [(16392, 2), 32693, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(291, 10928, F2, 3, 12) (dual of [(10928, 3), 32693, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(291, 8196, F2, 4, 12) (dual of [(8196, 4), 32693, 13]-NRT-code) | [i] | ||
| 7 | Linear OOA(291, 6556, F2, 5, 12) (dual of [(6556, 5), 32689, 13]-NRT-code) | [i] | ||
| 8 | Linear OOA(291, 5464, F2, 6, 12) (dual of [(5464, 6), 32693, 13]-NRT-code) | [i] | ||
| 9 | Linear OOA(291, 5464, F2, 7, 12) (dual of [(5464, 7), 38157, 13]-NRT-code) | [i] | OA Folding and Stacking | |
| 10 | Linear OOA(291, 5464, F2, 8, 12) (dual of [(5464, 8), 43621, 13]-NRT-code) | [i] | ||
| 11 | Linear OOA(291, 5464, F2, 12, 12) (dual of [(5464, 12), 65477, 13]-NRT-code) | [i] | ||