Information on Result #2790209
Linear OOA(2236, 4106, F2, 4, 33) (dual of [(4106, 4), 16188, 34]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2232, 4105, F2, 4, 33) (dual of [(4105, 4), 16188, 34]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2232, 16420, F2, 33) (dual of [16420, 16188, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(2225, 16385, F2, 33) (dual of [16385, 16160, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 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(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
- construction X applied to C([0,16]) ⊂ C([0,14]) [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(2236, 3485, F2, 5, 33) (dual of [(3485, 5), 17189, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2236, 3485, F2, 6, 33) (dual of [(3485, 6), 20674, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(2236, 3485, F2, 7, 33) (dual of [(3485, 7), 24159, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(2236, 3485, F2, 8, 33) (dual of [(3485, 8), 27644, 34]-NRT-code) | [i] | ||
| 5 | Digital (203, 236, 3485)-net over F2 | [i] | ||