Information on Result #2226784
Linear OA(2236, 530, F2, 56) (dual of [530, 294, 57]-code), using 1 times truncation based on linear OA(2237, 531, F2, 57) (dual of [531, 294, 58]-code), using
- construction XX applied to C1 = C([509,52]), C2 = C([0,54]), C3 = C1 + C2 = C([0,52]), and C∩ = C1 ∩ C2 = C([509,54]) [i] based on
- linear OA(2226, 511, F2, 55) (dual of [511, 285, 56]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,52}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(2226, 511, F2, 55) (dual of [511, 285, 56]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,54], and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(2235, 511, F2, 57) (dual of [511, 276, 58]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,54}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(2217, 511, F2, 53) (dual of [511, 294, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
- 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, using
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code) (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 OA(2256, 573, F2, 56) (dual of [573, 317, 57]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(2257, 578, F2, 56) (dual of [578, 321, 57]-code) | [i] | ||
| 3 | Linear OA(2258, 583, F2, 56) (dual of [583, 325, 57]-code) | [i] | ||
| 4 | Linear OA(2259, 589, F2, 56) (dual of [589, 330, 57]-code) | [i] | ||
| 5 | Linear OA(2260, 595, F2, 56) (dual of [595, 335, 57]-code) | [i] | ||
| 6 | Linear OOA(2236, 265, F2, 2, 56) (dual of [(265, 2), 294, 57]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2236, 176, F2, 3, 56) (dual of [(176, 3), 292, 57]-NRT-code) | [i] | ||
| 8 | Linear OOA(2236, 106, F2, 5, 56) (dual of [(106, 5), 294, 57]-NRT-code) | [i] | ||