Information on Result #2788404
Linear OOA(293, 8196, F2, 4, 13) (dual of [(8196, 4), 32691, 14]-NRT-code), using 21 times duplication based on linear OOA(292, 8196, F2, 4, 13) (dual of [(8196, 4), 32692, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(292, 32784, F2, 13) (dual of [32784, 32692, 14]-code), using
- construction X 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(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 X 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(293, 8196, F2, 5, 13) (dual of [(8196, 5), 40887, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(293, 8196, F2, 6, 13) (dual of [(8196, 6), 49083, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(293, 8196, F2, 7, 13) (dual of [(8196, 7), 57279, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(293, 8196, F2, 8, 13) (dual of [(8196, 8), 65475, 14]-NRT-code) | [i] | ||
| 5 | Digital (80, 93, 8196)-net over F2 | [i] | ||