Information on Result #2226707
Linear OA(2227, 530, F2, 54) (dual of [530, 303, 55]-code), using 1 times truncation based on linear OA(2228, 531, F2, 55) (dual of [531, 303, 56]-code), using
- construction XX applied to C1 = C([509,50]), C2 = C([0,52]), C3 = C1 + C2 = C([0,50]), and C∩ = C1 ∩ C2 = C([509,52]) [i] based on
- linear OA(2217, 511, F2, 53) (dual of [511, 294, 54]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,50}, and designed minimum distance d ≥ |I|+1 = 54 [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(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(2208, 511, F2, 51) (dual of [511, 303, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [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(2250, 579, F2, 54) (dual of [579, 329, 55]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(2251, 584, F2, 54) (dual of [584, 333, 55]-code) | [i] | ||
| 3 | Linear OA(2252, 589, F2, 54) (dual of [589, 337, 55]-code) | [i] | ||
| 4 | Linear OA(2253, 595, F2, 54) (dual of [595, 342, 55]-code) | [i] | ||
| 5 | Linear OA(2254, 601, F2, 54) (dual of [601, 347, 55]-code) | [i] | ||
| 6 | Linear OA(2255, 608, F2, 54) (dual of [608, 353, 55]-code) | [i] | ||
| 7 | Linear OA(2256, 615, F2, 54) (dual of [615, 359, 55]-code) | [i] | ||
| 8 | Linear OA(2257, 622, F2, 54) (dual of [622, 365, 55]-code) | [i] | ||
| 9 | Linear OA(2258, 629, F2, 54) (dual of [629, 371, 55]-code) | [i] | ||
| 10 | Linear OOA(2227, 265, F2, 2, 54) (dual of [(265, 2), 303, 55]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(2227, 176, F2, 3, 54) (dual of [(176, 3), 301, 55]-NRT-code) | [i] | ||
| 12 | Linear OOA(2227, 132, F2, 4, 54) (dual of [(132, 4), 301, 55]-NRT-code) | [i] | ||
| 13 | Linear OOA(2227, 106, F2, 5, 54) (dual of [(106, 5), 303, 55]-NRT-code) | [i] | ||