Information on Result #808594
Linear OOA(2198, 523, F2, 2, 40) (dual of [(523, 2), 848, 41]-NRT-code), using OOA 2-folding based on linear OA(2198, 1046, F2, 40) (dual of [1046, 848, 41]-code), using
- construction XX applied to C1 = C([1021,36]), C2 = C([1,38]), C3 = C1 + C2 = C([1,36]), and C∩ = C1 ∩ C2 = C([1021,38]) [i] based on
- linear OA(2186, 1023, F2, 39) (dual of [1023, 837, 40]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,36}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2185, 1023, F2, 38) (dual of [1023, 838, 39]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2196, 1023, F2, 41) (dual of [1023, 827, 42]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2175, 1023, F2, 36) (dual of [1023, 848, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
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(2198, 523, F2, 3, 40) (dual of [(523, 3), 1371, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2198, 523, F2, 4, 40) (dual of [(523, 4), 1894, 41]-NRT-code) | [i] | ||
| 3 | Linear OOA(2198, 523, F2, 5, 40) (dual of [(523, 5), 2417, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(2198, 523, F2, 6, 40) (dual of [(523, 6), 2940, 41]-NRT-code) | [i] | ||
| 5 | Linear OOA(2198, 523, F2, 7, 40) (dual of [(523, 7), 3463, 41]-NRT-code) | [i] | ||
| 6 | Linear OOA(2198, 523, F2, 8, 40) (dual of [(523, 8), 3986, 41]-NRT-code) | [i] | ||
| 7 | Digital (158, 198, 523)-net over F2 | [i] | ||