Information on Result #2610579
Linear OOA(279, 10929, F2, 3, 10) (dual of [(10929, 3), 32708, 11]-NRT-code), using strength reduction based on linear OOA(279, 10929, F2, 3, 11) (dual of [(10929, 3), 32708, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(279, 32787, F2, 11) (dual of [32787, 32708, 12]-code), using
- 2 times code embedding in larger space [i] based on linear OA(277, 32785, F2, 11) (dual of [32785, 32708, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- 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(261, 32768, F2, 9) (dual of [32768, 32707, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(10) ⊂ Ce(8) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(277, 32785, F2, 11) (dual of [32785, 32708, 12]-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(279, 10929, F2, 4, 10) (dual of [(10929, 4), 43637, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(279, 10929, F2, 5, 10) (dual of [(10929, 5), 54566, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(279, 10929, F2, 6, 10) (dual of [(10929, 6), 65495, 11]-NRT-code) | [i] | ||
| 4 | Linear OOA(279, 10929, F2, 7, 10) (dual of [(10929, 7), 76424, 11]-NRT-code) | [i] | ||
| 5 | Linear OOA(279, 10929, F2, 8, 10) (dual of [(10929, 8), 87353, 11]-NRT-code) | [i] | ||
| 6 | Digital (69, 79, 10929)-net over F2 | [i] | ||