Information on Result #1131451
Linear OOA(2154, 87384, F2, 6, 17) (dual of [(87384, 6), 524150, 18]-NRT-code), using OOA 6-folding based on linear OA(2154, 524304, F2, 17) (dual of [524304, 524150, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2154, 524308, F2, 17) (dual of [524308, 524154, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2153, 524288, F2, 17) (dual of [524288, 524135, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2134, 524288, F2, 15) (dual of [524288, 524154, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 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(16) ⊂ Ce(14) [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(2154, 87384, F2, 6, 16) (dual of [(87384, 6), 524150, 17]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2154, 87384, F2, 7, 17) (dual of [(87384, 7), 611534, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2154, 87384, F2, 8, 17) (dual of [(87384, 8), 698918, 18]-NRT-code) | [i] | ||
| 4 | Digital (137, 154, 87384)-net over F2 | [i] | ||