Information on Result #1053680
Linear OOA(2236, 8202, F2, 4, 31) (dual of [(8202, 4), 32572, 32]-NRT-code), using OOA 4-folding based on linear OA(2236, 32808, F2, 31) (dual of [32808, 32572, 32]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2233, 32805, F2, 31) (dual of [32805, 32572, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(2226, 32768, F2, 31) (dual of [32768, 32542, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(27, 37, F2, 3) (dual of [37, 30, 4]-code or 37-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 Ce(30) ⊂ Ce(26) [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, 8202, F2, 4, 30) (dual of [(8202, 4), 32572, 31]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2237, 8202, F2, 4, 31) (dual of [(8202, 4), 32571, 32]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2235, 8201, F2, 4, 30) (dual of [(8201, 4), 32569, 31]-NRT-code) | [i] | Truncation for OOAs | |