Information on Result #2666807
Linear OOA(296, 2736, F2, 3, 14) (dual of [(2736, 3), 8112, 15]-NRT-code), using 22 times duplication based on linear OOA(294, 2736, F2, 3, 14) (dual of [(2736, 3), 8114, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(294, 8208, F2, 14) (dual of [8208, 8114, 15]-code), using
- strength reduction [i] based on linear OA(294, 8208, F2, 15) (dual of [8208, 8114, 16]-code), using
- adding a parity check bit [i] based on linear OA(293, 8207, F2, 14) (dual of [8207, 8114, 15]-code), using
- construction X4 applied to C([0,14]) ⊂ C([1,12]) [i] based on
- linear OA(292, 8191, F2, 15) (dual of [8191, 8099, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(278, 8191, F2, 12) (dual of [8191, 8113, 13]-code), using 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(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
- construction X4 applied to C([0,14]) ⊂ C([1,12]) [i] based on
- adding a parity check bit [i] based on linear OA(293, 8207, F2, 14) (dual of [8207, 8114, 15]-code), using
- strength reduction [i] based on linear OA(294, 8208, F2, 15) (dual of [8208, 8114, 16]-code), 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 OOA(296, 2736, F2, 4, 14) (dual of [(2736, 4), 10848, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(296, 2736, F2, 5, 14) (dual of [(2736, 5), 13584, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(296, 2736, F2, 6, 14) (dual of [(2736, 6), 16320, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(296, 2736, F2, 7, 14) (dual of [(2736, 7), 19056, 15]-NRT-code) | [i] | ||
| 5 | Linear OOA(296, 2736, F2, 8, 14) (dual of [(2736, 8), 21792, 15]-NRT-code) | [i] | ||
| 6 | Digital (82, 96, 2736)-net over F2 | [i] | ||