Information on Result #1584296
Linear OOA(231, 32784, F2, 4, 4) (dual of [(32784, 4), 131105, 5]-NRT-code), using appending kth column based on linear OOA(231, 32784, F2, 3, 4) (dual of [(32784, 3), 98321, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(231, 32784, F2, 4) (dual of [32784, 32753, 5]-code), using
- 1 times truncation [i] based on linear OA(232, 32785, F2, 5) (dual of [32785, 32753, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(231, 32768, F2, 5) (dual of [32768, 32737, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(216, 32768, F2, 3) (dual of [32768, 32752, 4]-code or 32768-cap in PG(15,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(216, 17, F2, 15) (dual of [17, 1, 16]-code), using
- strength reduction [i] based on linear OA(216, 17, F2, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
- dual of repetition code with length 17 [i]
- strength reduction [i] based on linear OA(216, 17, F2, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
- linear OA(21, 17, F2, 1) (dual of [17, 16, 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(4) ⊂ Ce(2) [i] based on
- 1 times truncation [i] based on linear OA(232, 32785, F2, 5) (dual of [32785, 32753, 6]-code), using
Mode: 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(231, 32784, F2, 5, 4) (dual of [(32784, 5), 163889, 5]-NRT-code) | [i] | Appending Arbitrary Columns | |
| 2 | Linear OOA(231, 32784, F2, 6, 4) (dual of [(32784, 6), 196673, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(231, 32784, F2, 7, 4) (dual of [(32784, 7), 229457, 5]-NRT-code) | [i] | ||
| 4 | Linear OOA(231, 32784, F2, 8, 4) (dual of [(32784, 8), 262241, 5]-NRT-code) | [i] | ||
| 5 | Digital (27, 31, 32784)-net over F2 | [i] | Net Defined by OOA | |