Information on Result #806876
Linear OOA(2111, 266, F2, 2, 24) (dual of [(266, 2), 421, 25]-NRT-code), using OOA 2-folding based on linear OA(2111, 532, F2, 24) (dual of [532, 421, 25]-code), using
- construction XX applied to C1 = C([509,20]), C2 = C([1,22]), C3 = C1 + C2 = C([1,20]), and C∩ = C1 ∩ C2 = C([509,22]) [i] based on
- linear OA(2100, 511, F2, 23) (dual of [511, 411, 24]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,20}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(299, 511, F2, 22) (dual of [511, 412, 23]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2109, 511, F2, 25) (dual of [511, 402, 26]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,22}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(290, 511, F2, 20) (dual of [511, 421, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 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, using
- linear OA(21, 10, F2, 1) (dual of [10, 9, 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(2111, 266, F2, 3, 24) (dual of [(266, 3), 687, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2111, 266, F2, 4, 24) (dual of [(266, 4), 953, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(2111, 266, F2, 5, 24) (dual of [(266, 5), 1219, 25]-NRT-code) | [i] | ||
| 4 | Linear OOA(2111, 266, F2, 6, 24) (dual of [(266, 6), 1485, 25]-NRT-code) | [i] | ||
| 5 | Linear OOA(2111, 266, F2, 7, 24) (dual of [(266, 7), 1751, 25]-NRT-code) | [i] | ||
| 6 | Linear OOA(2111, 266, F2, 8, 24) (dual of [(266, 8), 2017, 25]-NRT-code) | [i] | ||
| 7 | Digital (87, 111, 266)-net over F2 | [i] | ||