Information on Result #2223689
Linear OA(2109, 262163, F2, 12) (dual of [262163, 262054, 13]-code), using 1 times truncation based on linear OA(2110, 262164, F2, 13) (dual of [262164, 262054, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(2109, 262144, F2, 13) (dual of [262144, 262035, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(291, 262144, F2, 11) (dual of [262144, 262053, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(219, 20, F2, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
- dual of repetition code with length 20 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 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(2111, 262165, F2, 12) (dual of [262165, 262054, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2112, 262166, F2, 12) (dual of [262166, 262054, 13]-code) | [i] | ||
| 3 | Linear OA(2113, 262167, F2, 12) (dual of [262167, 262054, 13]-code) | [i] | ||
| 4 | Linear OOA(2109, 131081, F2, 2, 12) (dual of [(131081, 2), 262053, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2109, 87387, F2, 3, 12) (dual of [(87387, 3), 262052, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(2109, 65540, F2, 4, 12) (dual of [(65540, 4), 262051, 13]-NRT-code) | [i] | ||
| 7 | Linear OOA(2109, 52432, F2, 5, 12) (dual of [(52432, 5), 262051, 13]-NRT-code) | [i] | ||
| 8 | Linear OOA(2109, 43693, F2, 6, 12) (dual of [(43693, 6), 262049, 13]-NRT-code) | [i] | ||
| 9 | Linear OOA(2109, 43693, F2, 7, 12) (dual of [(43693, 7), 305742, 13]-NRT-code) | [i] | OA Folding and Stacking | |
| 10 | Linear OOA(2109, 43693, F2, 8, 12) (dual of [(43693, 8), 349435, 13]-NRT-code) | [i] | ||
| 11 | Linear OOA(2109, 43693, F2, 12, 12) (dual of [(43693, 12), 524207, 13]-NRT-code) | [i] | ||