Information on Result #809074
Linear OOA(2218, 522, F2, 2, 45) (dual of [(522, 2), 826, 46]-NRT-code), using OOA 2-folding based on linear OA(2218, 1044, F2, 45) (dual of [1044, 826, 46]-code), using
- discarding factors / shortening the dual code based on linear OA(2218, 1045, F2, 45) (dual of [1045, 827, 46]-code), using
- construction XX applied to C1 = C([1021,40]), C2 = C([0,42]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([1021,42]) [i] based on
- linear OA(2206, 1023, F2, 43) (dual of [1023, 817, 44]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,40}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2206, 1023, F2, 43) (dual of [1023, 817, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2216, 1023, F2, 45) (dual of [1023, 807, 46]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,42}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2196, 1023, F2, 41) (dual of [1023, 827, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [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, 11, F2, 1) (dual of [11, 10, 2]-code) (see above)
- construction XX applied to C1 = C([1021,40]), C2 = C([0,42]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([1021,42]) [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(2218, 522, F2, 3, 45) (dual of [(522, 3), 1348, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2218, 522, F2, 4, 45) (dual of [(522, 4), 1870, 46]-NRT-code) | [i] | ||
| 3 | Linear OOA(2218, 522, F2, 5, 45) (dual of [(522, 5), 2392, 46]-NRT-code) | [i] | ||
| 4 | Linear OOA(2218, 522, F2, 6, 45) (dual of [(522, 6), 2914, 46]-NRT-code) | [i] | ||
| 5 | Linear OOA(2218, 522, F2, 7, 45) (dual of [(522, 7), 3436, 46]-NRT-code) | [i] | ||
| 6 | Linear OOA(2218, 522, F2, 8, 45) (dual of [(522, 8), 3958, 46]-NRT-code) | [i] | ||
| 7 | Digital (173, 218, 522)-net over F2 | [i] | ||