Information on Result #1053674
Linear OOA(2224, 4109, F2, 4, 31) (dual of [(4109, 4), 16212, 32]-NRT-code), using OOA 4-folding based on linear OA(2224, 16436, F2, 31) (dual of [16436, 16212, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2224, 16439, F2, 31) (dual of [16439, 16215, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2169, 16384, F2, 25) (dual of [16384, 16215, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(213, 55, F2, 5) (dual of [55, 42, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [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(2224, 4109, F2, 4, 30) (dual of [(4109, 4), 16212, 31]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2224, 3682, F2, 5, 31) (dual of [(3682, 5), 18186, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2224, 3682, F2, 6, 31) (dual of [(3682, 6), 21868, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(2224, 3682, F2, 7, 31) (dual of [(3682, 7), 25550, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(2224, 3682, F2, 8, 31) (dual of [(3682, 8), 29232, 32]-NRT-code) | [i] | ||
| 6 | Digital (193, 224, 3682)-net over F2 | [i] | ||