Information on Result #2221492
Linear OA(279, 8206, F2, 12) (dual of [8206, 8127, 13]-code), using 1 times truncation based on linear OA(280, 8207, F2, 13) (dual of [8207, 8127, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(279, 8192, F2, 13) (dual of [8192, 8113, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(266, 8192, F2, 11) (dual of [8192, 8126, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(214, 15, F2, 13) (dual of [15, 1, 14]-code), using
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- dual of repetition code with length 15 [i]
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(281, 8208, F2, 12) (dual of [8208, 8127, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(282, 8209, F2, 12) (dual of [8209, 8127, 13]-code) | [i] | ||
| 3 | Linear OA(283, 8210, F2, 12) (dual of [8210, 8127, 13]-code) | [i] | ||
| 4 | Linear OA(283, 8211, F2, 12) (dual of [8211, 8128, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(279, 4103, F2, 2, 12) (dual of [(4103, 2), 8127, 13]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(279, 2735, F2, 3, 12) (dual of [(2735, 3), 8126, 13]-NRT-code) | [i] | ||
| 7 | Linear OOA(279, 2051, F2, 4, 12) (dual of [(2051, 4), 8125, 13]-NRT-code) | [i] | ||
| 8 | Linear OOA(279, 1641, F2, 5, 12) (dual of [(1641, 5), 8126, 13]-NRT-code) | [i] | ||
| 9 | Linear OOA(279, 1367, F2, 6, 12) (dual of [(1367, 6), 8123, 13]-NRT-code) | [i] | ||
| 10 | Linear OOA(279, 1367, F2, 7, 12) (dual of [(1367, 7), 9490, 13]-NRT-code) | [i] | OA Folding and Stacking | |
| 11 | Linear OOA(279, 1367, F2, 8, 12) (dual of [(1367, 8), 10857, 13]-NRT-code) | [i] | ||
| 12 | Linear OOA(279, 1367, F2, 12, 12) (dual of [(1367, 12), 16325, 13]-NRT-code) | [i] | ||