Information on Result #702673
Linear OA(2246, 531, F2, 59) (dual of [531, 285, 60]-code), using construction XX applied to C1 = C([509,54]), C2 = C([0,56]), C3 = C1 + C2 = C([0,54]), and C∩ = C1 ∩ C2 = C([509,56]) based on
- 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(2235, 511, F2, 57) (dual of [511, 276, 58]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,56], and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(2244, 511, F2, 59) (dual of [511, 267, 60]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,56}, and designed minimum distance d ≥ |I|+1 = 60 [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(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(2245, 530, F2, 58) (dual of [530, 285, 59]-code) | [i] | Truncation | |
| 2 | Linear OOA(2246, 265, F2, 2, 59) (dual of [(265, 2), 284, 60]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2246, 177, F2, 3, 59) (dual of [(177, 3), 285, 60]-NRT-code) | [i] | ||
| 4 | Linear OOA(2246, 106, F2, 5, 59) (dual of [(106, 5), 284, 60]-NRT-code) | [i] | ||