Information on Result #2784601
Linear OOA(2205, 8201, F2, 4, 26) (dual of [(8201, 4), 32599, 27]-NRT-code), using 1 step truncation based on linear OOA(2206, 8202, F2, 4, 27) (dual of [(8202, 4), 32602, 28]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2206, 32808, F2, 27) (dual of [32808, 32602, 28]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2203, 32805, F2, 27) (dual of [32805, 32602, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- 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(2166, 32768, F2, 23) (dual of [32768, 32602, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(26) ⊂ Ce(22) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(2203, 32805, F2, 27) (dual of [32805, 32602, 28]-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(2205, 6573, F2, 5, 26) (dual of [(6573, 5), 32660, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2205, 6573, F2, 6, 26) (dual of [(6573, 6), 39233, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(2205, 6573, F2, 7, 26) (dual of [(6573, 7), 45806, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(2205, 6573, F2, 8, 26) (dual of [(6573, 8), 52379, 27]-NRT-code) | [i] | ||
| 5 | Digital (179, 205, 6573)-net over F2 | [i] | ||