Information on Result #703058
Linear OA(2258, 1045, F2, 53) (dual of [1045, 787, 54]-code), using construction XX applied to C1 = C([1021,48]), C2 = C([0,50]), C3 = C1 + C2 = C([0,48]), and C∩ = C1 ∩ C2 = C([1021,50]) based on
- linear OA(2246, 1023, F2, 51) (dual of [1023, 777, 52]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,48}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2246, 1023, F2, 51) (dual of [1023, 777, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2256, 1023, F2, 53) (dual of [1023, 767, 54]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,50}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(2236, 1023, F2, 49) (dual of [1023, 787, 50]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [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)
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(2257, 1044, F2, 52) (dual of [1044, 787, 53]-code) | [i] | Truncation | |
| 2 | Linear OOA(2258, 522, F2, 2, 53) (dual of [(522, 2), 786, 54]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2258, 348, F2, 3, 53) (dual of [(348, 3), 786, 54]-NRT-code) | [i] | ||
| 4 | Linear OOA(2258, 261, F2, 4, 53) (dual of [(261, 4), 786, 54]-NRT-code) | [i] | ||
| 5 | Linear OOA(2258, 209, F2, 5, 53) (dual of [(209, 5), 787, 54]-NRT-code) | [i] | ||
| 6 | Linear OOA(2258, 174, F2, 6, 53) (dual of [(174, 6), 786, 54]-NRT-code) | [i] | ||
| 7 | Linear OOA(2258, 149, F2, 7, 53) (dual of [(149, 7), 785, 54]-NRT-code) | [i] | ||