Information on Result #1096856
Linear OOA(2204, 3284, F2, 5, 29) (dual of [(3284, 5), 16216, 30]-NRT-code), using OOA 5-folding based on linear OA(2204, 16420, F2, 29) (dual of [16420, 16216, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- linear OA(2197, 16385, F2, 29) (dual of [16385, 16188, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2169, 16385, F2, 25) (dual of [16385, 16216, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(27, 35, F2, 3) (dual of [35, 28, 4]-code or 35-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), 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(2205, 3284, F2, 5, 29) (dual of [(3284, 5), 16215, 30]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2206, 3284, F2, 5, 29) (dual of [(3284, 5), 16214, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(2207, 3284, F2, 5, 29) (dual of [(3284, 5), 16213, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(2208, 3284, F2, 5, 29) (dual of [(3284, 5), 16212, 30]-NRT-code) | [i] | ||
| 5 | Linear OOA(2204, 3284, F2, 6, 29) (dual of [(3284, 6), 19500, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(2204, 3284, F2, 7, 29) (dual of [(3284, 7), 22784, 30]-NRT-code) | [i] | ||
| 7 | Linear OOA(2204, 3284, F2, 8, 29) (dual of [(3284, 8), 26068, 30]-NRT-code) | [i] | ||
| 8 | Digital (175, 204, 3284)-net over F2 | [i] | ||