Information on Result #1051485
Linear OOA(281, 2052, F2, 4, 13) (dual of [(2052, 4), 8127, 14]-NRT-code), using OOA 4-folding based on linear OA(281, 8208, F2, 13) (dual of [8208, 8127, 14]-code), using
- 1 times code embedding in larger space [i] 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
- construction X4 applied to Ce(12) ⊂ Ce(10) [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(282, 2052, F2, 4, 13) (dual of [(2052, 4), 8126, 14]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(283, 2052, F2, 4, 13) (dual of [(2052, 4), 8125, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(284, 2052, F2, 4, 13) (dual of [(2052, 4), 8124, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(281, 2052, F2, 5, 13) (dual of [(2052, 5), 10179, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(281, 2052, F2, 6, 13) (dual of [(2052, 6), 12231, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(281, 2052, F2, 7, 13) (dual of [(2052, 7), 14283, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(281, 2052, F2, 8, 13) (dual of [(2052, 8), 16335, 14]-NRT-code) | [i] | ||
| 8 | Digital (68, 81, 2052)-net over F2 | [i] | ||