Information on Result #2790095
Linear OOA(2234, 4105, F2, 4, 32) (dual of [(4105, 4), 16186, 33]-NRT-code), using 22 times duplication based on linear OOA(2232, 4105, F2, 4, 32) (dual of [(4105, 4), 16188, 33]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2232, 16420, F2, 32) (dual of [16420, 16188, 33]-code), using
- strength reduction [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
- strength reduction [i] based on linear OA(2232, 16420, F2, 33) (dual of [16420, 16188, 34]-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(2234, 3967, F2, 5, 32) (dual of [(3967, 5), 19601, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2234, 3967, F2, 6, 32) (dual of [(3967, 6), 23568, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(2234, 3967, F2, 7, 32) (dual of [(3967, 7), 27535, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(2234, 3967, F2, 8, 32) (dual of [(3967, 8), 31502, 33]-NRT-code) | [i] | ||
| 5 | Digital (202, 234, 3967)-net over F2 | [i] | ||